GST_report/2023-08-20_15-35-39_XYICphase_L8_hessian_exact_errorbar
generated by pyGSTi on November 29, 2023
Summary
Welcome to a pyGSTi analysis report! This report is organized into tabs
, each of which is accessible from the sidebar on the left. This Summary tab summarizes the most popular analyses and figures of merit. Much more detailed analysis is available on other tabs. If this report encapsulates multiple datasets, estimates, or gauges, then you can switch between those using the dropdown menus on the sidebar. For more information about how to use this report, click on the Help tab link to the left.
starrating shown in the Model Violation tab.
| Gate | Entanglement Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Eigenvalue Ent. Infidelity | Eigenvalue 1/2 Diamond-Dist |
|---|---|---|---|---|---|
| [] | 0.004518 ± 0.003354 | 0.008601 ± 0.015255 | 0.010213 ± 0.024067 | 0.004518 ± 0.003354 | 0.014303 ± 0.005622 |
| Gxpi2:1 | 0.004066 ± 0.00333 | 0.008238 ± 0.008764 | 0.011578 ± 0.016654 | 0.004042 ± 0.003323 | 0.007118 ± 0.012143 |
| Gxpi2:0 | 0.00576 ± 0.003517 | 0.020257 ± 0.008829 | 0.027131 ± 0.023717 | 0.005686 ± 0.003515 | 0.036384 ± 0.016394 |
| Gypi2:1 | 0.006353 ± 0.004823 | 0.016997 ± 0.008889 | 0.024357 ± 0.025227 | 0.006272 ± 0.004786 | 0.023633 ± 0.016052 |
| Gypi2:0 | 0.010279 ± 0.004381 | 0.026744 ± 0.011663 | 0.035214 ± 0.044543 | 0.010169 ± 0.004379 | 0.044374 ± 0.023966 |
| Gcphase:0:1 | 0.023373 ± 0.006443 | 0.044264 ± 0.007059 | 0.061999 ± 0.03809 | 0.023202 ± 0.006445 | 0.080889 ± 0.009068 |
| Gate | Entanglement Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Eigenvalue Ent. Infidelity | Eigenvalue 1/2 Diamond-Dist |
|---|---|---|---|---|---|
| [] | 0.008327 ± 0.004118 | 0.013126 ± 0.113007 | 0.015144 ± 0.013637 | 0.008327 ± 0.004118 | 0.022465 ± 0.050942 |
| Gxpi2:1 | 0.009474 ± 0.003728 | 0.01249 ± 0.005867 | 0.014506 ± 0.03951 | 0.009442 ± 0.003714 | 0.016893 ± 0.00917 |
| Gxpi2:0 | 0.008635 ± 0.006525 | 0.026421 ± 0.007359 | 0.034333 ± 0.043641 | 0.008543 ± 0.006499 | 0.052543 ± 0.015301 |
| Gypi2:1 | 0.010377 ± 0.007077 | 0.02524 ± 0.007416 | 0.031271 ± 0.016447 | 0.010279 ± 0.007086 | 0.036754 ± 0.054848 |
| Gypi2:0 | 0.010939 ± 0.005013 | 0.028377 ± 0.016611 | 0.036155 ± 0.002875 | 0.010826 ± 0.004919 | 0.054397 ± 0.026701 |
| Gcphase:0:1 | 0.018755 ± 0.005138 | 0.042103 ± 0.005652 | 0.048942 ± 0.047235 | 0.018634 ± 0.005214 | 0.077814 ± 0.048129 |
| Gate | Entanglement Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Eigenvalue Ent. Infidelity | Eigenvalue 1/2 Diamond-Dist |
|---|---|---|---|---|---|
| [] | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:1 | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:0 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:1 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:0 | 0 | 0 | 0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 | 0 | 0 | 0 |
Model Violation Analysis
The plots and tables on this tab summarize how well the GST estimate actually fits the data. Although they may be less familiar to you than, say, process fidelity, these analyses are essential to understanding the GST estimate, and how much to trust it! Real qubit systems often display behavior that isn't consistent with modeling each gate as a stationary CPTP map. When pyGSTi tries to fit such data to its model (a single gateset), this "non-Markovianity" manifests as model violation. This tab provides several views of the model violation observed for this fit, ranging from the coarse-grained (total violation) to hyper-detailed (per-circuit violation). More observed model violation ⇒ the error metrics on other tabs should be trusted less.
starrating found in a later table detailing the overall model violation.
| L | 2Δ(log L) | k | 2Δ(log L)-k | √2k | Nsigma | Ns | Np | Rating |
|---|---|---|---|---|---|---|---|---|
| 1 | 2342.024 | 1125 | 1217.024 | 47.43416 | 25.7 | 2388 | 1263 | ★★★ |
| 2 | 3104.192 | 1669 | 1435.192 | 57.77543 | 24.8 | 2931 | 1262 | ★★★ |
| 4 | 4525.096 | 2633 | 1892.096 | 72.56721 | 26.1 | 3888 | 1255 | ★★★ |
| 8 | 6629.969 | 3850 | 2779.969 | 87.74964 | 31.7 | 5106 | 1256 | ★★★ |
| L | 2Δ(log L) | k | 2Δ(log L)-k | √2k | Nsigma | Ns | Np | Rating |
|---|---|---|---|---|---|---|---|---|
| 1 | 5713.009 | 2169 | 3544.009 | 65.8635 | 53.8 | 2388 | 219 | ★★★ |
| 2 | 7080.589 | 2713 | 4367.589 | 73.66139 | 59.3 | 2931 | 218 | ★★★ |
| 4 | 9545.768 | 3671 | 5874.768 | 85.68547 | 68.6 | 3888 | 217 | ★★★ |
| 8 | 13590.57 | 4892 | 8698.573 | 98.9141 | 87.9 | 5106 | 214 | ★★★ |
| L | 2Δ(log L) | k | 2Δ(log L)-k | √2k | Nsigma | Ns | Np | Rating |
|---|---|---|---|---|---|---|---|---|
| 1 | 303924.2 | 2214 | 301710.2 | 66.54322 | 5×103 | 2388 | 174 | ★ |
| 2 | 387138.1 | 2757 | 384381.1 | 74.25631 | 5×103 | 2931 | 174 | ★ |
| 4 | 537975.4 | 3714 | 534261.4 | 86.18585 | 6×103 | 3888 | 174 | ★ |
| 8 | 737897.6 | 4932 | 732965.6 | 99.31767 | 7×103 | 5106 | 174 | ★ |
Model violation for each individual circuit
This tab presents the second of two statistical tests available to detect that a dataset violates pyGSTi's Markovian gateset model. The first is based on the aggregate loglikelihood score presented elsewhere. This tab shows the individual loglikelihood scores for each circuit in the dataset. Each circuit is represented by a colored box, whose color indicates how badly this estimate (model) failed to predict the observed outcome frequencies of that circuit. Light gray indicates consistency with the model, dark gray indicates possible -- but statistically insignificant -- inconsistency, and red squares indicate circuits whose outcomes are inconsistent with the model at the family-wise 95 percent confidence level. In other words, if data are generated by a Markovian gateset, then with 95%% probability every box will be gray. Even a single red square thus represents a clear detection of model violation. When many squares are red, their pattern can provide useful diagnostic clues to what kind of non-Markovian noise is present.
plaquette) corresponds to a particular germ-power "base sequence", and each pixel within a block corresponds to a specific "fiducial pair" -- i.e., choice of pre- and post-fiducial sequences. The base sequences are arranged by germ (varying from row to row), and by power/length (varying from column to column). Hovering over a colored box will pop up the exact circuit to which it corresponds, the observed frequencies, and the corresponding probabilities predicted by the GST estimate of the gateset. The slider below the figure permits switching between different estimates, labeled by L, which were obtained from subsets of the data that included only base sequences of length up to L.
plaquette) corresponds to a particular germ-power "base sequence", and each pixel within a block corresponds to a specific "fiducial pair" -- i.e., choice of pre- and post-fiducial sequences. The base sequences are arranged by germ (varying from row to row), and by power/length (varying from column to column). Hovering over a colored box will pop up the exact circuit to which it corresponds, the observed frequencies, and the corresponding probabilities predicted by the GST estimate of the gateset. The slider below the figure permits switching between different estimates, labeled by L, which were obtained from subsets of the data that included only base sequences of length up to L.
Gauge Invariant Error Metrics
GST can estimate gates up to an overall gauge. PyGSTi tries to find a good gauge in which to report process matrices and gauge-variant metrics like fidelity -- but sometimes this goes wrong. The most reliable error metrics and gate properties are gauge-invariant ones, and these are listed on this tab.
Direct RB(DRB). DRB allows for sampling layers of primitives according to a general probability distribution over the primitive gates; the number reported here corresponds to uniformly sampling the primitive gates. This number does not require any compilation table and is always be computed by pyGSTi. Two caveats regarding these RB numbers: 1) The primitive RB number is not meaningful for arbitrary gate sets; if the gate set generates the Clifford group or it is a universal gate set then it is definitely meaningful, modulo the second caveat. 2) These predicted RB numbers rely on a perturbative technique, and if the estimated gates are far from their ideal counterparts the predicted numbers may be very inaccurate (and the empirical RB error rate itself may even be ill-defined: the RB decay could be non-exponential). For both of these RB protocols there is also more than one definition of the RB number, as a function of the p obtained from fitting RB data to A + Bp^m. Here we use the definition r = (4^n - 1)(1-p)/4^n for an n-qubit gate set, which means that r = entanglement infidelity = 1/2 diamond distance if there are uniform depolarizing errors on all the gates (where these two quantities are w.r.t. the gate set benchmarked, so the Clifford gates for CRB and the primitive gates for DRB). For more general errors, these first two quantities will often be roughly equal, although that is not guaranteed. Note that these numbers should not be directly compared to RB numbers derived using the commonly-used alternative formula r = (2^n - 1)(1-p)/2^n (which is related to average gate infidelity, rather than entanglement infidelity).
| Metric | Value |
|---|---|
| Predicted primitive RB number | -1 ± 0 |
| Metric | Value |
|---|---|
| Predicted primitive RB number | -1 ± 0 |
| Metric | Value |
|---|---|
| Predicted primitive RB number | -1 |
| 00 | 01 | 10 | 11 | |
|---|---|---|---|---|
| Target ρ0 | 1 | 0 | 0 | 0 |
| Estimated ρ0 | 0.939965 ± 0.005793 | 0.036672 ± 0.004731 | 0.021212 ± 0.003836 | 0.002151 ± 0.002117 |
| 00 | 01 | 10 | 11 | |
|---|---|---|---|---|
| Target ρ0 | 1 | 0 | 0 | 0 |
| Estimated ρ0 | 0.868819 ± 0.006996 | 0.056221 ± 0.005766 | 0.059755 ± 0.005981 | 0.015205 ± 0.004949 |
| 00 | 01 | 10 | 11 | |
|---|---|---|---|---|
| Target ρ0 | 1 | 0 | 0 | 0 |
| Estimated ρ0 | 1 | 0 | 0 | 0 |
| Gate | Eigenvalue Ent. Infidelity | Eigenvalue Avg. Gate Infidelity | Eigenvalue Non-U. Ent. Infidelity | Eigenvalue Non-U. Avg. Gate Infidelity | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|---|---|---|---|
| [] | 0.004518 | 0.003615 | 0.004485 | 0.003588 | 0.014303 | 0.006135 |
| Gxpi2:1 | 0.004042 | 0.003234 | 0.004035 | 0.003228 | 0.007118 | 0.007118 |
| Gxpi2:0 | 0.005686 | 0.004549 | 0.005442 | 0.004353 | 0.036384 | 0.008071 |
| Gypi2:1 | 0.006272 | 0.005017 | 0.006172 | 0.004938 | 0.023633 | 0.009257 |
| Gypi2:0 | 0.010169 | 0.008135 | 0.009764 | 0.007811 | 0.044374 | 0.016027 |
| Gcphase:0:1 | 0.023202 | 0.018562 | 0.022392 | 0.017914 | 0.080889 | 0.039705 |
| Gate | Eigenvalue Ent. Infidelity | Eigenvalue Avg. Gate Infidelity | Eigenvalue Non-U. Ent. Infidelity | Eigenvalue Non-U. Avg. Gate Infidelity | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|---|---|---|---|
| [] | 0.008327 | 0.006662 | 0.008258 | 0.006606 | 0.022465 | 0.013276 |
| Gxpi2:1 | 0.009442 | 0.007554 | 0.009442 | 0.007554 | 0.016893 | 0.016865 |
| Gxpi2:0 | 0.008543 | 0.006835 | 0.00814 | 0.006512 | 0.052543 | 0.010909 |
| Gypi2:1 | 0.010279 | 0.008223 | 0.010002 | 0.008002 | 0.036754 | 0.015572 |
| Gypi2:0 | 0.010826 | 0.008661 | 0.010341 | 0.008273 | 0.054397 | 0.015888 |
| Gcphase:0:1 | 0.018634 | 0.014907 | 0.017678 | 0.014143 | 0.077814 | 0.030349 |
| Gate | Eigenvalue Ent. Infidelity | Eigenvalue Avg. Gate Infidelity | Eigenvalue Non-U. Ent. Infidelity | Eigenvalue Non-U. Avg. Gate Infidelity | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|---|---|---|---|
| [] | 0 | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Eigenvalue Ent. Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.004518 | 0.008327 | 0 |
| Gxpi2:1 | 0.004042 | 0.009442 | 0 |
| Gxpi2:0 | 0.005686 | 0.008543 | 0 |
| Gypi2:1 | 0.006272 | 0.010279 | 0 |
| Gypi2:0 | 0.010169 | 0.010826 | 0 |
| Gcphase:0:1 | 0.023202 | 0.018634 | 0 |
| Eigenvalue Avg. Gate Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.003615 | 0.006662 | 0 |
| Gxpi2:1 | 0.003234 | 0.007554 | 0 |
| Gxpi2:0 | 0.004549 | 0.006835 | 0 |
| Gypi2:1 | 0.005017 | 0.008223 | 0 |
| Gypi2:0 | 0.008135 | 0.008661 | 0 |
| Gcphase:0:1 | 0.018562 | 0.014907 | 0 |
| Eigenvalue Non-U. Ent. Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.004485 | 0.008258 | 0 |
| Gxpi2:1 | 0.004035 | 0.009442 | 0 |
| Gxpi2:0 | 0.005442 | 0.00814 | 0 |
| Gypi2:1 | 0.006172 | 0.010002 | 0 |
| Gypi2:0 | 0.009764 | 0.010341 | 0 |
| Gcphase:0:1 | 0.022392 | 0.017678 | 0 |
| Eigenvalue Non-U. Avg. Gate Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.003588 | 0.006606 | 0 |
| Gxpi2:1 | 0.003228 | 0.007554 | 0 |
| Gxpi2:0 | 0.004353 | 0.006512 | 0 |
| Gypi2:1 | 0.004938 | 0.008002 | 0 |
| Gypi2:0 | 0.007811 | 0.008273 | 0 |
| Gcphase:0:1 | 0.017914 | 0.014143 | 0 |
| Eigenvalue 1/2 Diamond-Dist | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.014303 | 0.022465 | 0 |
| Gxpi2:1 | 0.007118 | 0.016893 | 0 |
| Gxpi2:0 | 0.036384 | 0.052543 | 0 |
| Gypi2:1 | 0.023633 | 0.036754 | 0 |
| Gypi2:0 | 0.044374 | 0.054397 | 0 |
| Gcphase:0:1 | 0.080889 | 0.077814 | 0 |
| Eigenvalue Non-U. 1/2 Diamond-Dist | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.006135 | 0.013276 | 0 |
| Gxpi2:1 | 0.007118 | 0.016865 | 0 |
| Gxpi2:0 | 0.008071 | 0.010909 | 0 |
| Gypi2:1 | 0.009257 | 0.015572 | 0 |
| Gypi2:0 | 0.016027 | 0.015888 | 0 |
| Gcphase:0:1 | 0.039705 | 0.030349 | 0 |
| Blank |
|---|
| Gate | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197e^{i0.127\pi} \\ 0.033197e^{i0.127\pi} \\ 0.06558e^{i0.106\pi} \\ 0.06558e^{i0.106\pi} \\ 0.08755e^{i0.308\pi} \\ 0.08755e^{i0.308\pi} \\ 0.047392e^{i0.128\pi} \\ 0.047392e^{i0.128\pi} \\ 0.088316e^{i0.181\pi} \\ 0.088316e^{i0.181\pi} \\ 0.104669e^{i0.227\pi} \\ 0.104669e^{i0.227\pi} \\ 0.082095e^{i0.329\pi} \\ 0.082095e^{i0.329\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003209 \\ 0.015257 \\ 0.015257 \\ 0.007848 \\ 0.007848 \\ 0.008827 \\ 0.008827 \\ 0.013092 \\ 0.013092 \\ 0.005341 \\ 0.005341 \\ 0.005993 \\ 0.005993 \\ 0.009735 \\ 0.009735 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197 \\ 0.033197 \\ 0.06558 \\ 0.06558 \\ 0.08755 \\ 0.08755 \\ 0.047392 \\ 0.047392 \\ 0.088316 \\ 0.088316 \\ 0.104669 \\ 0.104669 \\ 0.082095 \\ 0.082095 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003209 \\ 0.003579 \\ 0.003579 \\ 0.004219 \\ 0.004219 \\ 0.004645 \\ 0.004645 \\ 0.004834 \\ 0.004834 \\ 0.005301 \\ 0.005301 \\ 0.005396 \\ 0.005396 \\ 0.00657 \\ 0.00657 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.0306 \\ 0.0306 \\ 0.06198 \\ 0.06198 \\ 0.049648 \\ 0.049648 \\ 0.043599 \\ 0.043599 \\ 0.074394 \\ 0.074394 \\ 0.07909 \\ 0.07909 \\ 0.042094 \\ 0.042094 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.003214 \\ -0.003475 \\ -0.003475 \\ -0.004206 \\ -0.004206 \\ -0.004627 \\ -0.004627 \\ -0.004771 \\ -0.004771 \\ -0.005315 \\ -0.005315 \\ -0.005407 \\ -0.005407 \\ -0.006566 \\ -0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ -0.004737 \\ 0.002115 \\ -0.002115 \\ 0.002401 \\ -0.002401 \\ 0.003891 \\ -0.003891 \\ 0.000208 \\ -0.000208 \\ 0.000835 \\ -0.000835 \\ 0.002301 \\ -0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.003214 \\ 0.003475 \\ 0.003475 \\ 0.004206 \\ 0.004206 \\ 0.004627 \\ 0.004627 \\ 0.004771 \\ 0.004771 \\ 0.005315 \\ 0.005315 \\ 0.005407 \\ 0.005407 \\ 0.006566 \\ 0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ 0.004737 \\ 0.002115 \\ 0.002115 \\ 0.002401 \\ 0.002401 \\ 0.003891 \\ 0.003891 \\ 0.000208 \\ 0.000208 \\ 0.000835 \\ 0.000835 \\ 0.002301 \\ 0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116e^{i0.286\pi} \\ 0.013116e^{i0.286\pi} \\ 0.012005e^{i0.190\pi} \\ 0.012005e^{i0.190\pi} \\ 0.036209 \\ 0.019967 \\ 0.025786e^{i0.090\pi} \\ 0.025786e^{i0.090\pi} \\ 0.024928e^{i0.343\pi} \\ 0.024928e^{i0.343\pi} \\ 0.011678e^{i0.195\pi} \\ 0.011678e^{i0.195\pi} \\ 0.013669e^{i0.278\pi} \\ 0.013669e^{i0.278\pi} \\ 0.012952 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.006895 \\ 0.006895 \\ 0.003185 \\ 0.003185 \\ 0.003383 \\ 0.003653 \\ 0.006167 \\ 0.006167 \\ 0.007136 \\ 0.007136 \\ 0.005224 \\ 0.005224 \\ 0.006774 \\ 0.006774 \\ 0.007593 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116 \\ 0.013116 \\ 0.012005 \\ 0.012005 \\ 0.036209 \\ 0.019967 \\ 0.025786 \\ 0.025786 \\ 0.024928 \\ 0.024928 \\ 0.011678 \\ 0.011678 \\ 0.013669 \\ 0.013669 \\ 0.012952 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002538 \\ 0.002538 \\ 0.002756 \\ 0.002756 \\ 0.003383 \\ 0.003653 \\ 0.003946 \\ 0.003946 \\ 0.004775 \\ 0.004775 \\ 0.005211 \\ 0.005211 \\ 0.005797 \\ 0.005797 \\ 0.007593 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008171 \\ 0.008171 \\ 0.009921 \\ 0.009921 \\ 0.036209 \\ 0.019967 \\ 0.024767 \\ 0.024767 \\ 0.011794 \\ 0.011794 \\ 0.009546 \\ 0.009546 \\ 0.008785 \\ 0.008785 \\ 0.012952 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.00252 \\ -0.00252 \\ -0.002758 \\ -0.002758 \\ -0.003389 \\ -0.003659 \\ -0.003942 \\ -0.003942 \\ -0.004773 \\ -0.004773 \\ -0.005225 \\ -0.005225 \\ -0.005807 \\ -0.005807 \\ -0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ -0.01025 \\ 0.006821 \\ -0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ -0.006734 \\ 0.010485 \\ -0.010581 \\ 0.012967 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.497954 \\ -0.497954 \\ 0.499491 \\ -0.499491 \\ 0 \\ 0 \\ 0.001515 \\ -0.001515 \\ 0.001696 \\ -0.001696 \\ 0.499883 \\ -0.499883 \\ 0.501122 \\ -0.501122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.00256 \\ 0.002656 \\ -0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ -0.003033 \\ 0.003076 \\ -0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.00252 \\ 0.00252 \\ 0.002758 \\ 0.002758 \\ 0.003389 \\ 0.003659 \\ 0.003942 \\ 0.003942 \\ 0.004773 \\ 0.004773 \\ 0.005225 \\ 0.005225 \\ 0.005807 \\ 0.005807 \\ 0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ 0.01025 \\ 0.006821 \\ 0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ 0.006734 \\ 0.010485 \\ 0.010581 \\ 0.012967 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002046 \\ 0.002046 \\ 0.000509 \\ 0.000509 \\ 0 \\ 0 \\ 0.001515 \\ 0.001515 \\ 0.001696 \\ 0.001696 \\ 0.000117 \\ 0.000117 \\ 0.001122 \\ 0.001122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.00256 \\ 0.002656 \\ 0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ 0.003033 \\ 0.003076 \\ 0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491e^{i0.149\pi} \\ 0.009491e^{i0.149\pi} \\ 0.010889e^{i0.135\pi} \\ 0.010889e^{i0.135\pi} \\ 0.005753 \\ 0.017147 \\ 0.035739e^{i0.334\pi} \\ 0.035739e^{i0.334\pi} \\ 0.018055e^{i0.326\pi} \\ 0.018055e^{i0.326\pi} \\ 0.038498e^{i0.377\pi} \\ 0.038498e^{i0.377\pi} \\ 0.030343e^{i0.369\pi} \\ 0.030343e^{i0.369\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002498 \\ 0.010953 \\ 0.010953 \\ 0.007579 \\ 0.007579 \\ 0.004259 \\ 0.006157 \\ 0.03881 \\ 0.03881 \\ 0.029408 \\ 0.029408 \\ 0.031842 \\ 0.031842 \\ 0.02383 \\ 0.02383 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491 \\ 0.009491 \\ 0.010889 \\ 0.010889 \\ 0.005753 \\ 0.017147 \\ 0.035739 \\ 0.035739 \\ 0.018055 \\ 0.018055 \\ 0.038498 \\ 0.038498 \\ 0.030343 \\ 0.030343 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002498 \\ 0.003679 \\ 0.003679 \\ 0.003854 \\ 0.003854 \\ 0.004259 \\ 0.006157 \\ 0.007198 \\ 0.007198 \\ 0.007013 \\ 0.007013 \\ 0.008433 \\ 0.008433 \\ 0.008856 \\ 0.008856 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.008473 \\ 0.008473 \\ 0.009919 \\ 0.009919 \\ 0.005753 \\ 0.017147 \\ 0.017759 \\ 0.017759 \\ 0.009373 \\ 0.009373 \\ 0.014459 \\ 0.014459 \\ 0.012147 \\ 0.012147 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002501 \\ -0.003632 \\ -0.003632 \\ -0.00384 \\ -0.00384 \\ -0.004269 \\ -0.006176 \\ -0.006487 \\ -0.006487 \\ -0.006624 \\ -0.006624 \\ -0.00799 \\ -0.00799 \\ -0.008646 \\ -0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ -0.004353 \\ 0.004484 \\ -0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ -0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ -0.028072 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.503296 \\ -0.503296 \\ 0.502085 \\ -0.502085 \\ 0 \\ 0 \\ 0.512221 \\ -0.512221 \\ 0.009152 \\ -0.009152 \\ 0.009854 \\ -0.009854 \\ 0.492896 \\ -0.492896 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002709 \\ 0.002704 \\ -0.003165 \\ 0.003175 \\ 0 \\ 0 \\ -0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ -0.003598 \\ 0.004215 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002501 \\ 0.003632 \\ 0.003632 \\ 0.00384 \\ 0.00384 \\ 0.004269 \\ 0.006176 \\ 0.006487 \\ 0.006487 \\ 0.006624 \\ 0.006624 \\ 0.00799 \\ 0.00799 \\ 0.008646 \\ 0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ 0.004353 \\ 0.004484 \\ 0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ 0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ 0.028072 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.003296 \\ 0.003296 \\ 0.002085 \\ 0.002085 \\ 0 \\ 0 \\ 0.012221 \\ 0.012221 \\ 0.009152 \\ 0.009152 \\ 0.009854 \\ 0.009854 \\ 0.007104 \\ 0.007104 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002709 \\ 0.002704 \\ 0.003165 \\ 0.003175 \\ 0 \\ 0 \\ 0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ 0.003598 \\ 0.004215 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921e^{i0.147\pi} \\ 0.013921e^{i0.147\pi} \\ 0.020085e^{i0.333\pi} \\ 0.020085e^{i0.333\pi} \\ 0.02497e^{i0.247\pi} \\ 0.02497e^{i0.247\pi} \\ 0.006584e^{i0.249\pi} \\ 0.006584e^{i0.249\pi} \\ 0.042272 \\ 0.038761 \\ 0.038939e^{i0.081\pi} \\ 0.038939e^{i0.081\pi} \\ 0.01071e^{i0.226\pi} \\ 0.01071e^{i0.226\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003738 \\ 0.005208 \\ 0.005208 \\ 0.016016 \\ 0.016016 \\ 0.025208 \\ 0.025208 \\ 0.019955 \\ 0.019955 \\ 0.006655 \\ 0.008251 \\ 0.020756 \\ 0.020756 \\ 0.010144 \\ 0.010144 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921 \\ 0.013921 \\ 0.020085 \\ 0.020085 \\ 0.02497 \\ 0.02497 \\ 0.006584 \\ 0.006584 \\ 0.042272 \\ 0.038761 \\ 0.038939 \\ 0.038939 \\ 0.01071 \\ 0.01071 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003738 \\ 0.004337 \\ 0.004337 \\ 0.005119 \\ 0.005119 \\ 0.006075 \\ 0.006075 \\ 0.006022 \\ 0.006022 \\ 0.006655 \\ 0.008251 \\ 0.009422 \\ 0.009422 \\ 0.009877 \\ 0.009877 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.012461 \\ 0.012461 \\ 0.010068 \\ 0.010068 \\ 0.017847 \\ 0.017847 \\ 0.004665 \\ 0.004665 \\ 0.042272 \\ 0.038761 \\ 0.037691 \\ 0.037691 \\ 0.008129 \\ 0.008129 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.003745 \\ -0.004342 \\ -0.004342 \\ -0.005016 \\ -0.005016 \\ -0.005791 \\ -0.005791 \\ -0.005857 \\ -0.005857 \\ -0.006677 \\ -0.008286 \\ -0.009293 \\ -0.009293 \\ -0.009923 \\ -0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ -0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ -0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ -0.009901 \\ 0.007071 \\ -0.007015 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.500922 \\ -0.500922 \\ 0.004855 \\ -0.004855 \\ 0.007834 \\ -0.007834 \\ 0.493908 \\ -0.493908 \\ 0 \\ 0 \\ 0.505942 \\ -0.505942 \\ 0.499257 \\ -0.499257 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ -0.001458 \\ 0.001529 \\ 0 \\ 0 \\ -0.01205 \\ 0.012172 \\ -0.00259 \\ 0.002637 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.003745 \\ 0.004342 \\ 0.004342 \\ 0.005016 \\ 0.005016 \\ 0.005791 \\ 0.005791 \\ 0.005857 \\ 0.005857 \\ 0.006677 \\ 0.008286 \\ 0.009293 \\ 0.009293 \\ 0.009923 \\ 0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ 0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ 0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ 0.009901 \\ 0.007071 \\ 0.007015 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.000922 \\ 0.000922 \\ 0.004855 \\ 0.004855 \\ 0.007834 \\ 0.007834 \\ 0.006092 \\ 0.006092 \\ 0 \\ 0 \\ 0.005942 \\ 0.005942 \\ 0.000743 \\ 0.000743 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ 0.001458 \\ 0.001529 \\ 0 \\ 0 \\ 0.01205 \\ 0.012172 \\ 0.00259 \\ 0.002637 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552e^{i0.352\pi} \\ 0.016552e^{i0.352\pi} \\ 0.009933e^{i0.202\pi} \\ 0.009933e^{i0.202\pi} \\ 0.016999e^{i0.132\pi} \\ 0.016999e^{i0.132\pi} \\ 0.023078 \\ 0.004973e^{i0.076\pi} \\ 0.004973e^{i0.076\pi} \\ 0.03488e^{i0.248\pi} \\ 0.03488e^{i0.248\pi} \\ 0.030281e^{i0.308\pi} \\ 0.030281e^{i0.308\pi} \\ 0.044571e^{i0.343\pi} \\ 0.044571e^{i0.343\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004505 \\ 0.004505 \\ 0.005523 \\ 0.005523 \\ 0.008997 \\ 0.008997 \\ 0.00883 \\ 0.045408 \\ 0.045408 \\ 0.047332 \\ 0.047332 \\ 0.036861 \\ 0.036861 \\ 0.038701 \\ 0.038701 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552 \\ 0.016552 \\ 0.009933 \\ 0.009933 \\ 0.016999 \\ 0.016999 \\ 0.023078 \\ 0.004973 \\ 0.004973 \\ 0.03488 \\ 0.03488 \\ 0.030281 \\ 0.030281 \\ 0.044571 \\ 0.044571 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004481 \\ 0.004481 \\ 0.004526 \\ 0.004526 \\ 0.006776 \\ 0.006776 \\ 0.00883 \\ 0.0131 \\ 0.0131 \\ 0.013861 \\ 0.013861 \\ 0.016496 \\ 0.016496 \\ 0.017699 \\ 0.017699 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007431 \\ 0.007431 \\ 0.007995 \\ 0.007995 \\ 0.015552 \\ 0.015552 \\ 0.023078 \\ 0.004834 \\ 0.004834 \\ 0.024824 \\ 0.024824 \\ 0.017204 \\ 0.017204 \\ 0.021099 \\ 0.021099 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.004491 \\ -0.004491 \\ -0.004531 \\ -0.004531 \\ -0.006781 \\ -0.006781 \\ -0.008869 \\ -0.012217 \\ -0.012217 \\ -0.012906 \\ -0.012906 \\ -0.016072 \\ -0.016072 \\ -0.017244 \\ -0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ -0.005932 \\ 0.006915 \\ -0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ -0.025988 \\ 0.025696 \\ -0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000148 \\ -0.000148 \\ 0.501012 \\ -0.501012 \\ 0.501897 \\ -0.501897 \\ 0 \\ 0.014014 \\ -0.014014 \\ 0.514598 \\ -0.514598 \\ 0.489335 \\ -0.489335 \\ 0.011148 \\ -0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ -0.002547 \\ 0.002566 \\ -0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ -0.008163 \\ 0.007836 \\ -0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.004491 \\ 0.004491 \\ 0.004531 \\ 0.004531 \\ 0.006781 \\ 0.006781 \\ 0.008869 \\ 0.012217 \\ 0.012217 \\ 0.012906 \\ 0.012906 \\ 0.016072 \\ 0.016072 \\ 0.017244 \\ 0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ 0.005932 \\ 0.006915 \\ 0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ 0.025988 \\ 0.025696 \\ 0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000148 \\ 0.000148 \\ 0.001012 \\ 0.001012 \\ 0.001897 \\ 0.001897 \\ 0 \\ 0.014014 \\ 0.014014 \\ 0.014598 \\ 0.014598 \\ 0.010665 \\ 0.010665 \\ 0.011148 \\ 0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ 0.002547 \\ 0.002566 \\ 0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ 0.008163 \\ 0.007836 \\ 0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165e^{i0.337\pi} \\ 0.057165e^{i0.337\pi} \\ 0.016817e^{i0.290\pi} \\ 0.016817e^{i0.290\pi} \\ 0.025934e^{i0.183\pi} \\ 0.025934e^{i0.183\pi} \\ 0.045487e^{i0.269\pi} \\ 0.045487e^{i0.269\pi} \\ 0.073076e^{i0.319\pi} \\ 0.073076e^{i0.319\pi} \\ 0.026551e^{i0.378\pi} \\ 0.026551e^{i0.378\pi} \\ 0.021225e^{i0.085\pi} \\ 0.021225e^{i0.085\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003883 \\ 0.033357 \\ 0.033357 \\ 0.054973 \\ 0.054973 \\ 0.021034 \\ 0.021034 \\ 0.05589 \\ 0.05589 \\ 0.035539 \\ 0.035539 \\ 0.035696 \\ 0.035696 \\ 0.086282 \\ 0.086282 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165 \\ 0.057165 \\ 0.016817 \\ 0.016817 \\ 0.025934 \\ 0.025934 \\ 0.045487 \\ 0.045487 \\ 0.073076 \\ 0.073076 \\ 0.026551 \\ 0.026551 \\ 0.021225 \\ 0.021225 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003883 \\ 0.016637 \\ 0.016637 \\ 0.018116 \\ 0.018116 \\ 0.020857 \\ 0.020857 \\ 0.025191 \\ 0.025191 \\ 0.028452 \\ 0.028452 \\ 0.029246 \\ 0.029246 \\ 0.045177 \\ 0.045177 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.028062 \\ 0.028062 \\ 0.010301 \\ 0.010301 \\ 0.021772 \\ 0.021772 \\ 0.030165 \\ 0.030165 \\ 0.039399 \\ 0.039399 \\ 0.009896 \\ 0.009896 \\ 0.020473 \\ 0.020473 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.00389 \\ -0.016345 \\ -0.016345 \\ -0.016887 \\ -0.016887 \\ -0.021074 \\ -0.021074 \\ -0.024206 \\ -0.024206 \\ -0.028625 \\ -0.028625 \\ -0.02946 \\ -0.02946 \\ -0.043275 \\ -0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ -0.009696 \\ -0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ -0.009368 \\ -0.010459 \\ -0.021059 \\ -0.021996 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ -0.009356 \\ 0.98319 \\ -0.98319 \\ 0.000884 \\ -0.000884 \\ 0.016277 \\ -0.016277 \\ 0.006976 \\ -0.006976 \\ 0.99329 \\ -0.99329 \\ 0.975543 \\ -0.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ -0.004517 \\ -0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ -0.008221 \\ 1.991908 \\ -0.002428 \\ -0.001362 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.00389 \\ 0.016345 \\ 0.016345 \\ 0.016887 \\ 0.016887 \\ 0.021074 \\ 0.021074 \\ 0.024206 \\ 0.024206 \\ 0.028625 \\ 0.028625 \\ 0.02946 \\ 0.02946 \\ 0.043275 \\ 0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ 0.009696 \\ 0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ 0.009368 \\ 0.010459 \\ 0.021059 \\ 0.021996 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ 0.009356 \\ 0.01681 \\ 1.98319 \\ 0.000884 \\ 0.000884 \\ 0.016277 \\ 0.016277 \\ 0.006976 \\ 0.006976 \\ 0.00671 \\ 1.99329 \\ 0.024457 \\ 1.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ 0.004517 \\ 0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ 0.008221 \\ 1.991908 \\ 0.002428 \\ 0.001362 \end{pmatrix} $ π |
| Gate | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222e^{i0.422\pi} \\ 0.02222e^{i0.422\pi} \\ 0.046623e^{i0.386\pi} \\ 0.046623e^{i0.386\pi} \\ 0.042233e^{i0.370\pi} \\ 0.042233e^{i0.370\pi} \\ 0.099689 \\ 0.070182e^{i0.296\pi} \\ 0.070182e^{i0.296\pi} \\ 0.05523e^{i0.308\pi} \\ 0.05523e^{i0.308\pi} \\ 0.06728e^{i0.202\pi} \\ 0.06728e^{i0.202\pi} \\ 0.046658e^{i0.368\pi} \\ 0.046658e^{i0.368\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001292 \\ 0.001292 \\ 0.01045 \\ 0.01045 \\ 0.019453 \\ 0.019453 \\ 0.007394 \\ 0.014434 \\ 0.014434 \\ 0.011967 \\ 0.011967 \\ 0.015754 \\ 0.015754 \\ 0.023963 \\ 0.023963 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222 \\ 0.02222 \\ 0.046623 \\ 0.046623 \\ 0.042233 \\ 0.042233 \\ 0.099689 \\ 0.070182 \\ 0.070182 \\ 0.05523 \\ 0.05523 \\ 0.06728 \\ 0.06728 \\ 0.046658 \\ 0.046658 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001286 \\ 0.001286 \\ 0.006151 \\ 0.006151 \\ 0.006301 \\ 0.006301 \\ 0.007394 \\ 0.008823 \\ 0.008823 \\ 0.011927 \\ 0.011927 \\ 0.014084 \\ 0.014084 \\ 0.014348 \\ 0.014348 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005405 \\ 0.005405 \\ 0.016356 \\ 0.016356 \\ 0.016764 \\ 0.016764 \\ 0.099689 \\ 0.04192 \\ 0.04192 \\ 0.031377 \\ 0.031377 \\ 0.054243 \\ 0.054243 \\ 0.018749 \\ 0.018749 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001287 \\ -0.001287 \\ -0.006134 \\ -0.006134 \\ -0.00615 \\ -0.00615 \\ -0.007422 \\ -0.008796 \\ -0.008796 \\ -0.011998 \\ -0.011998 \\ -0.014159 \\ -0.014159 \\ -0.014262 \\ -0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000039 \\ -0.000039 \\ 0.002706 \\ -0.002706 \\ 0.005895 \\ -0.005895 \\ 0 \\ 0.003668 \\ -0.003668 \\ 0.000315 \\ -0.000315 \\ 0.002279 \\ -0.002279 \\ 0.006197 \\ -0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001287 \\ 0.001287 \\ 0.006134 \\ 0.006134 \\ 0.00615 \\ 0.00615 \\ 0.007422 \\ 0.008796 \\ 0.008796 \\ 0.011998 \\ 0.011998 \\ 0.014159 \\ 0.014159 \\ 0.014262 \\ 0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000039 \\ 0.000039 \\ 0.002706 \\ 0.002706 \\ 0.005895 \\ 0.005895 \\ 0 \\ 0.003668 \\ 0.003668 \\ 0.000315 \\ 0.000315 \\ 0.002279 \\ 0.002279 \\ 0.006197 \\ 0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203e^{i0.125\pi} \\ 0.009203e^{i0.125\pi} \\ 0.01311e^{i0.170\pi} \\ 0.01311e^{i0.170\pi} \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025e^{i0.364\pi} \\ 0.031025e^{i0.364\pi} \\ 0.044919e^{i0.256\pi} \\ 0.044919e^{i0.256\pi} \\ 0.02034e^{i0.335\pi} \\ 0.02034e^{i0.335\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.0013 \\ 0.003727 \\ 0.003727 \\ 0.003884 \\ 0.003884 \\ 0.004938 \\ 0.007481 \\ 0.011582 \\ 0.014083 \\ 0.015019 \\ 0.015019 \\ 0.015412 \\ 0.015412 \\ 0.018019 \\ 0.018019 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203 \\ 0.009203 \\ 0.01311 \\ 0.01311 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025 \\ 0.031025 \\ 0.044919 \\ 0.044919 \\ 0.02034 \\ 0.02034 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.0013 \\ 0.003682 \\ 0.003682 \\ 0.003796 \\ 0.003796 \\ 0.004938 \\ 0.007481 \\ 0.011582 \\ 0.014083 \\ 0.014999 \\ 0.014999 \\ 0.015378 \\ 0.015378 \\ 0.01799 \\ 0.01799 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.008497 \\ 0.008497 \\ 0.011286 \\ 0.011286 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.012828 \\ 0.012828 \\ 0.031168 \\ 0.031168 \\ 0.010067 \\ 0.010067 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001301 \\ -0.003689 \\ -0.003689 \\ -0.003803 \\ -0.003803 \\ -0.00495 \\ -0.007509 \\ -0.011649 \\ -0.014183 \\ -0.015112 \\ -0.015112 \\ -0.015497 \\ -0.015497 \\ -0.018153 \\ -0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ -0.003522 \\ 0.006745 \\ -0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ -0.029019 \\ 0.032824 \\ -0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.500184 \\ -0.500184 \\ 0.499738 \\ -0.499738 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.500251 \\ -0.500251 \\ 0.499672 \\ -0.499672 \\ 0.000331 \\ -0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002706 \\ 0.002724 \\ -0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ -0.004037 \\ 0.00426 \\ -0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001301 \\ 0.003689 \\ 0.003689 \\ 0.003803 \\ 0.003803 \\ 0.00495 \\ 0.007509 \\ 0.011649 \\ 0.014183 \\ 0.015112 \\ 0.015112 \\ 0.015497 \\ 0.015497 \\ 0.018153 \\ 0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ 0.003522 \\ 0.006745 \\ 0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ 0.029019 \\ 0.032824 \\ 0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.000184 \\ 0.000184 \\ 0.000262 \\ 0.000262 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.000251 \\ 0.000251 \\ 0.000328 \\ 0.000328 \\ 0.000331 \\ 0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002706 \\ 0.002724 \\ 0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.004037 \\ 0.00426 \\ 0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449e^{i0.334\pi} \\ 0.008449e^{i0.334\pi} \\ 0.012314e^{i0.259\pi} \\ 0.012314e^{i0.259\pi} \\ 0.034277e^{i0.312\pi} \\ 0.034277e^{i0.312\pi} \\ 0.024184e^{i0.192\pi} \\ 0.024184e^{i0.192\pi} \\ 0.034863e^{i0.265\pi} \\ 0.034863e^{i0.265\pi} \\ 0.009148 \\ 0.055108e^{i0.418\pi} \\ 0.055108e^{i0.418\pi} \\ 0.013582 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002136 \\ 0.017216 \\ 0.017216 \\ 0.035663 \\ 0.035663 \\ 0.056046 \\ 0.056046 \\ 0.010865 \\ 0.010865 \\ 0.03961 \\ 0.03961 \\ 0.010278 \\ 0.023267 \\ 0.023267 \\ 0.011636 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449 \\ 0.008449 \\ 0.012314 \\ 0.012314 \\ 0.034277 \\ 0.034277 \\ 0.024184 \\ 0.024184 \\ 0.034863 \\ 0.034863 \\ 0.009148 \\ 0.055108 \\ 0.055108 \\ 0.013582 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002136 \\ 0.006364 \\ 0.006364 \\ 0.006919 \\ 0.006919 \\ 0.011581 \\ 0.011581 \\ 0.010074 \\ 0.010074 \\ 0.010819 \\ 0.010819 \\ 0.010278 \\ 0.010565 \\ 0.010565 \\ 0.011636 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.004209 \\ 0.004209 \\ 0.008451 \\ 0.008451 \\ 0.019081 \\ 0.019081 \\ 0.019931 \\ 0.019931 \\ 0.023446 \\ 0.023446 \\ 0.009148 \\ 0.01411 \\ 0.01411 \\ 0.013582 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002138 \\ -0.006255 \\ -0.006255 \\ -0.006322 \\ -0.006322 \\ -0.010112 \\ -0.010112 \\ -0.010117 \\ -0.010117 \\ -0.010136 \\ -0.010136 \\ -0.010331 \\ -0.010402 \\ -0.010402 \\ -0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ -0.007458 \\ 0.008709 \\ -0.009316 \\ 0.027483 \\ -0.030075 \\ 0.01402 \\ -0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.505124 \\ -0.505124 \\ 0.511209 \\ -0.511209 \\ 0.517641 \\ -0.517641 \\ 0.498692 \\ -0.498692 \\ 0.012255 \\ -0.012255 \\ 0 \\ 0.006668 \\ -0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.001376 \\ 0.00132 \\ -0.002782 \\ 0.002629 \\ -0.006454 \\ 0.005791 \\ -0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002138 \\ 0.006255 \\ 0.006255 \\ 0.006322 \\ 0.006322 \\ 0.010112 \\ 0.010112 \\ 0.010117 \\ 0.010117 \\ 0.010136 \\ 0.010136 \\ 0.010331 \\ 0.010402 \\ 0.010402 \\ 0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ 0.007458 \\ 0.008709 \\ 0.009316 \\ 0.027483 \\ 0.030075 \\ 0.01402 \\ 0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.005124 \\ 0.005124 \\ 0.011209 \\ 0.011209 \\ 0.017641 \\ 0.017641 \\ 0.001308 \\ 0.001308 \\ 0.012255 \\ 0.012255 \\ 0 \\ 0.006668 \\ 0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.001376 \\ 0.00132 \\ 0.002782 \\ 0.002629 \\ 0.006454 \\ 0.005791 \\ 0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056e^{i0.308\pi} \\ 0.016056e^{i0.308\pi} \\ 0.030592e^{i0.157\pi} \\ 0.030592e^{i0.157\pi} \\ 0.034405e^{i0.146\pi} \\ 0.034405e^{i0.146\pi} \\ 0.062388e^{i0.187\pi} \\ 0.062388e^{i0.187\pi} \\ 0.040223e^{i0.084\pi} \\ 0.040223e^{i0.084\pi} \\ 0.014925 \\ 0.121571e^{i0.056\pi} \\ 0.121571e^{i0.056\pi} \\ 0.063247 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002965 \\ 0.007242 \\ 0.007242 \\ 0.030046 \\ 0.030046 \\ 0.038711 \\ 0.038711 \\ 0.039205 \\ 0.039205 \\ 0.030259 \\ 0.030259 \\ 0.014356 \\ 0.016418 \\ 0.016418 \\ 0.01661 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056 \\ 0.016056 \\ 0.030592 \\ 0.030592 \\ 0.034405 \\ 0.034405 \\ 0.062388 \\ 0.062388 \\ 0.040223 \\ 0.040223 \\ 0.014925 \\ 0.121571 \\ 0.121571 \\ 0.063247 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002965 \\ 0.005471 \\ 0.005471 \\ 0.010116 \\ 0.010116 \\ 0.010728 \\ 0.010728 \\ 0.011736 \\ 0.011736 \\ 0.011475 \\ 0.011475 \\ 0.014356 \\ 0.015742 \\ 0.015742 \\ 0.01661 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.009126 \\ 0.009126 \\ 0.026929 \\ 0.026929 \\ 0.030827 \\ 0.030827 \\ 0.051969 \\ 0.051969 \\ 0.038834 \\ 0.038834 \\ 0.014925 \\ 0.119683 \\ 0.119683 \\ 0.063247 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002969 \\ -0.005475 \\ -0.005475 \\ -0.009759 \\ -0.009759 \\ -0.01008 \\ -0.01008 \\ -0.01109 \\ -0.01109 \\ -0.011141 \\ -0.011141 \\ -0.01446 \\ -0.015856 \\ -0.015856 \\ -0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ -0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ -0.036151 \\ 0.012379 \\ -0.008731 \\ 0.015028 \\ 0.02794 \\ -0.01485 \\ 0.062332 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.501519 \\ -0.501519 \\ 0.009095 \\ -0.009095 \\ 0.011962 \\ -0.011962 \\ 0.512043 \\ -0.512043 \\ 0.490987 \\ -0.490987 \\ 0 \\ 0.501508 \\ -0.501508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ -0.016574 \\ 0.016902 \\ -0.01225 \\ 0.012704 \\ 0 \\ -0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002969 \\ 0.005475 \\ 0.005475 \\ 0.009759 \\ 0.009759 \\ 0.01008 \\ 0.01008 \\ 0.01109 \\ 0.01109 \\ 0.011141 \\ 0.011141 \\ 0.01446 \\ 0.015856 \\ 0.015856 \\ 0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ 0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ 0.036151 \\ 0.012379 \\ 0.008731 \\ 0.015028 \\ 0.02794 \\ 0.01485 \\ 0.062332 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.001519 \\ 0.001519 \\ 0.009095 \\ 0.009095 \\ 0.011962 \\ 0.011962 \\ 0.012043 \\ 0.012043 \\ 0.009013 \\ 0.009013 \\ 0 \\ 0.001508 \\ 0.001508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ 0.016574 \\ 0.016902 \\ 0.01225 \\ 0.012704 \\ 0 \\ 0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424e^{i0.187\pi} \\ 0.009424e^{i0.187\pi} \\ 0.021644e^{i0.074\pi} \\ 0.021644e^{i0.074\pi} \\ 0.02175 \\ 0.034408 \\ 0.059387e^{i0.446\pi} \\ 0.059387e^{i0.446\pi} \\ 0.074565e^{i0.208\pi} \\ 0.074565e^{i0.208\pi} \\ 0.041644e^{i0.259\pi} \\ 0.041644e^{i0.259\pi} \\ 0.042314e^{i0.321\pi} \\ 0.042314e^{i0.321\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.009903 \\ 0.009903 \\ 0.022719 \\ 0.022719 \\ 0.007127 \\ 0.007299 \\ 0.058024 \\ 0.058024 \\ 0.048601 \\ 0.048601 \\ 0.03821 \\ 0.03821 \\ 0.029641 \\ 0.029641 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424 \\ 0.009424 \\ 0.021644 \\ 0.021644 \\ 0.02175 \\ 0.034408 \\ 0.059387 \\ 0.059387 \\ 0.074565 \\ 0.074565 \\ 0.041644 \\ 0.041644 \\ 0.042314 \\ 0.042314 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.003948 \\ 0.003948 \\ 0.004236 \\ 0.004236 \\ 0.007127 \\ 0.007299 \\ 0.018201 \\ 0.018201 \\ 0.017745 \\ 0.017745 \\ 0.017523 \\ 0.017523 \\ 0.017243 \\ 0.017243 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.007847 \\ 0.007847 \\ 0.021059 \\ 0.021059 \\ 0.02175 \\ 0.034408 \\ 0.009971 \\ 0.009971 \\ 0.059271 \\ 0.059271 \\ 0.028645 \\ 0.028645 \\ 0.022563 \\ 0.022563 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.000998 \\ -0.003914 \\ -0.003914 \\ -0.003994 \\ -0.003994 \\ -0.007153 \\ -0.007326 \\ -0.016796 \\ -0.016796 \\ -0.016845 \\ -0.016845 \\ -0.017082 \\ -0.017082 \\ -0.017093 \\ -0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ -0.005293 \\ 0.004755 \\ -0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ -0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ -0.036192 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.502902 \\ -0.502902 \\ 0.507134 \\ -0.507134 \\ 0 \\ 0 \\ 0.517844 \\ -0.517844 \\ 0.014652 \\ -0.014652 \\ 0.010997 \\ -0.010997 \\ 0.492193 \\ -0.492193 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00251 \\ 0.002506 \\ -0.006733 \\ 0.006729 \\ 0 \\ 0 \\ -0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ -0.006768 \\ 0.007868 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.003914 \\ 0.003914 \\ 0.003994 \\ 0.003994 \\ 0.007153 \\ 0.007326 \\ 0.016796 \\ 0.016796 \\ 0.016845 \\ 0.016845 \\ 0.017082 \\ 0.017082 \\ 0.017093 \\ 0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ 0.005293 \\ 0.004755 \\ 0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ 0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ 0.036192 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.002902 \\ 0.002902 \\ 0.007134 \\ 0.007134 \\ 0 \\ 0 \\ 0.017844 \\ 0.017844 \\ 0.014652 \\ 0.014652 \\ 0.010997 \\ 0.010997 \\ 0.007807 \\ 0.007807 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00251 \\ 0.002506 \\ 0.006733 \\ 0.006729 \\ 0 \\ 0 \\ 0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ 0.006768 \\ 0.007868 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446e^{i0.154\pi} \\ 0.05446e^{i0.154\pi} \\ 0.029927e^{i0.115\pi} \\ 0.029927e^{i0.115\pi} \\ 0.026108e^{i0.316\pi} \\ 0.026108e^{i0.316\pi} \\ 0.060803e^{i0.249\pi} \\ 0.060803e^{i0.249\pi} \\ 0.045035e^{i0.412\pi} \\ 0.045035e^{i0.412\pi} \\ 0.096531e^{i0.422\pi} \\ 0.096531e^{i0.422\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001443 \\ 0.004749 \\ 0.006384 \\ 0.055819 \\ 0.055819 \\ 0.034317 \\ 0.034317 \\ 0.060234 \\ 0.060234 \\ 0.083001 \\ 0.083001 \\ 0.039018 \\ 0.039018 \\ 0.042665 \\ 0.042665 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446 \\ 0.05446 \\ 0.029927 \\ 0.029927 \\ 0.026108 \\ 0.026108 \\ 0.060803 \\ 0.060803 \\ 0.045035 \\ 0.045035 \\ 0.096531 \\ 0.096531 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001443 \\ 0.004749 \\ 0.006384 \\ 0.018752 \\ 0.018752 \\ 0.017878 \\ 0.017878 \\ 0.019618 \\ 0.019618 \\ 0.021639 \\ 0.021639 \\ 0.032134 \\ 0.032134 \\ 0.032759 \\ 0.032759 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.048212 \\ 0.048212 \\ 0.027979 \\ 0.027979 \\ 0.014237 \\ 0.014237 \\ 0.043157 \\ 0.043157 \\ 0.012358 \\ 0.012358 \\ 0.023429 \\ 0.023429 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001445 \\ -0.00476 \\ -0.006405 \\ -0.017497 \\ -0.017497 \\ -0.017595 \\ -0.017595 \\ -0.018129 \\ -0.018129 \\ -0.018533 \\ -0.018533 \\ -0.0324 \\ -0.0324 \\ -0.032908 \\ -0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ -0.012995 \\ -0.015655 \\ -0.039888 \\ -0.047663 \\ 0.014649 \\ 0.012659 \\ -0.016771 \\ -0.022458 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ -0.017039 \\ 0.009491 \\ -0.009491 \\ 0.98153 \\ -0.98153 \\ 0.973987 \\ -0.973987 \\ 0.007277 \\ -0.007277 \\ 0.991007 \\ -0.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ -0.007446 \\ -0.006922 \\ -0.0156 \\ -0.013324 \\ 0.013941 \\ 0.014152 \\ -0.031587 \\ 1.96868 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001445 \\ 0.00476 \\ 0.006405 \\ 0.017497 \\ 0.017497 \\ 0.017595 \\ 0.017595 \\ 0.018129 \\ 0.018129 \\ 0.018533 \\ 0.018533 \\ 0.0324 \\ 0.0324 \\ 0.032908 \\ 0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ 0.012995 \\ 0.015655 \\ 0.039888 \\ 0.047663 \\ 0.014649 \\ 0.012659 \\ 0.016771 \\ 0.022458 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ 0.017039 \\ 0.009491 \\ 0.009491 \\ 0.01847 \\ 1.98153 \\ 0.026013 \\ 1.973987 \\ 0.007277 \\ 0.007277 \\ 0.008993 \\ 1.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ 0.007446 \\ 0.006922 \\ 0.0156 \\ 0.013324 \\ 0.013941 \\ 0.014152 \\ 0.031587 \\ 1.96868 \end{pmatrix} $ π |
| Gate | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gate | M - I | FinvF([]) - I | FinvF(Gxpi2:1) - I | FinvF(Gxpi2:0) - I | FinvF(Gypi2:1) - I | FinvF(Gypi2:0) - I | FinvF(Gcphase:0:1) - I |
|---|---|---|---|---|---|---|---|
| [] | 0 | ||||||
| Gxpi2:1 | 0 | ||||||
| Gxpi2:0 | 0 | ||||||
| Gypi2:1 | 0 | ||||||
| Gypi2:0 | 0 | ||||||
| Gcphase:0:1 | 0 |
| Gate | M - I | FinvF([]) - I | FinvF(Gxpi2:1) - I | FinvF(Gxpi2:0) - I | FinvF(Gypi2:1) - I | FinvF(Gypi2:0) - I | FinvF(Gcphase:0:1) - I |
|---|---|---|---|---|---|---|---|
| [] | 0 | ||||||
| Gxpi2:1 | 0 | ||||||
| Gxpi2:0 | 0 | ||||||
| Gypi2:1 | 0 | ||||||
| Gypi2:0 | 0 | ||||||
| Gcphase:0:1 | 0 |
| Gate | M - I | FinvF([]) - I | FinvF(Gxpi2:1) - I | FinvF(Gxpi2:0) - I | FinvF(Gypi2:1) - I | FinvF(Gypi2:0) - I | FinvF(Gcphase:0:1) - I |
|---|---|---|---|---|---|---|---|
| [] | 0 | ||||||
| Gxpi2:1 | 0 | ||||||
| Gxpi2:0 | 0 | ||||||
| Gypi2:1 | 0 | ||||||
| Gypi2:0 | 0 | ||||||
| Gcphase:0:1 | 0 |
Gauge Invariant Error Metrics applied to germ sequences
All of the per-gate gauge-invariant metrics of the previous tab are functions of each gate's spectrum and do not account for how the gate relates to other gates. In an attempt to extract some of that information in a gauge-invariant way, this tab looks at the spectra of the germ-sequences. Each germ amplifies (i.e. has eigenvalues which correspond to) certain directions in gate-set space
. Some of these directions describe how the single gates relate to one another, and, if an amplificationally complete set of germs was used, every direction is amplified by at least one germ. This implies that the (gauge-invariant) spectra of the germs should constitute a full description of the gate set. This tab compares each germ-spectrum to the spectrum of that germ if it were generated using the set eigenspace-projected
gates obtained by placing each gate's GST-estimated eigenvalues within eigenbasis of the ideal target gate.
| Gate or Germ | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|
| [] | 0 | 0 |
| Gxpi2:1 | 0 | 0 |
| Gxpi2:0 | 0 | 0 |
| Gypi2:1 | 0 | 0 |
| Gypi2:0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0.010514 | 0.001904 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0.008299 | 0.001254 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0.012225 | 0.001578 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0.009757 | 0.001532 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0.024956 | 0.003869 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0.011029 | 0.004865 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0.024539 | 0.00877 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0.012957 | 0.003363 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0.050109 | 0.006693 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0.013449 | 0.004776 |
| Gate or Germ | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|
| [] | 0 | 0 |
| Gxpi2:1 | 0 | 0 |
| Gxpi2:0 | 0 | 0 |
| Gypi2:1 | 0 | 0 |
| Gypi2:0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0.019953 | 0.003005 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0.009737 | 0.008516 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0.026028 | 0.003653 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0.017317 | 0.004963 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0.028133 | 0.000847 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0.022401 | 0.008463 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0.037555 | 0.019163 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0.016009 | 0.001262 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0.043232 | 0.022142 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0.014294 | 0.00939 |
| Gate or Germ | Eigenvalue 1/2 Diamond-Dist | Eigenvalue Non-U. 1/2 Diamond-Dist |
|---|---|---|
| [] | 0 | 0 |
| Gxpi2:1 | 0 | 0 |
| Gxpi2:0 | 0 | 0 |
| Gypi2:1 | 0 | 0 |
| Gypi2:0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0 | 0 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0 | 0 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0 | 0 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0 | 0 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0 | 0 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0 | 0 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0 | 0 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0 | 0 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0 | 0 |
eigenspace-projectedgates (see elsewhere on this tab). If the individual gates' eigenvalues account for all imperfections, then the estimated and predicted germ spectra should be equal. Since spectra aren't ordered, the eigenvalues need to be matched up or aligned somehow. PyGSTi does this by identifying a minimum-weight matching based on the metric being computed. Mathematical descriptions of the metrics appear when hovering over the column headers.
| Gate or Germ | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197e^{i0.127\pi} \\ 0.033197e^{i0.127\pi} \\ 0.06558e^{i0.106\pi} \\ 0.06558e^{i0.106\pi} \\ 0.08755e^{i0.308\pi} \\ 0.08755e^{i0.308\pi} \\ 0.047392e^{i0.128\pi} \\ 0.047392e^{i0.128\pi} \\ 0.088316e^{i0.181\pi} \\ 0.088316e^{i0.181\pi} \\ 0.104669e^{i0.227\pi} \\ 0.104669e^{i0.227\pi} \\ 0.082095e^{i0.329\pi} \\ 0.082095e^{i0.329\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197 \\ 0.033197 \\ 0.06558 \\ 0.06558 \\ 0.08755 \\ 0.08755 \\ 0.047392 \\ 0.047392 \\ 0.088316 \\ 0.088316 \\ 0.104669 \\ 0.104669 \\ 0.082095 \\ 0.082095 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.006408 \\ 0.006925 \\ 0.006925 \\ 0.008376 \\ 0.008376 \\ 0.009211 \\ 0.009211 \\ 0.009497 \\ 0.009497 \\ 0.010573 \\ 0.010573 \\ 0.010755 \\ 0.010755 \\ 0.013046 \\ 0.013046 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015758 \\ 0.030944 \\ 0.030037 \\ 0.062128 \\ 0.061308 \\ 0.04979 \\ 0.049045 \\ 0.043918 \\ 0.042858 \\ 0.074048 \\ 0.073951 \\ 0.07887 \\ 0.078457 \\ 0.04212 \\ 0.041515 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.003214 \\ -0.003475 \\ -0.003475 \\ -0.004206 \\ -0.004206 \\ -0.004627 \\ -0.004627 \\ -0.004771 \\ -0.004771 \\ -0.005315 \\ -0.005315 \\ -0.005407 \\ -0.005407 \\ -0.006566 \\ -0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ -0.004737 \\ 0.002115 \\ -0.002115 \\ 0.002401 \\ -0.002401 \\ 0.003891 \\ -0.003891 \\ 0.000208 \\ -0.000208 \\ 0.000835 \\ -0.000835 \\ 0.002301 \\ -0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116e^{i0.286\pi} \\ 0.013116e^{i0.286\pi} \\ 0.012005e^{i0.190\pi} \\ 0.012005e^{i0.190\pi} \\ 0.036209 \\ 0.019967 \\ 0.025786e^{i0.090\pi} \\ 0.025786e^{i0.090\pi} \\ 0.024928e^{i0.343\pi} \\ 0.024928e^{i0.343\pi} \\ 0.011678e^{i0.195\pi} \\ 0.011678e^{i0.195\pi} \\ 0.013669e^{i0.278\pi} \\ 0.013669e^{i0.278\pi} \\ 0.012952 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116 \\ 0.013116 \\ 0.012005 \\ 0.012005 \\ 0.036209 \\ 0.019967 \\ 0.025786 \\ 0.025786 \\ 0.024928 \\ 0.024928 \\ 0.011678 \\ 0.011678 \\ 0.013669 \\ 0.013669 \\ 0.012952 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.005028 \\ 0.005028 \\ 0.005501 \\ 0.005501 \\ 0.006755 \\ 0.007292 \\ 0.007853 \\ 0.007853 \\ 0.0095 \\ 0.0095 \\ 0.010395 \\ 0.010395 \\ 0.011548 \\ 0.011548 \\ 0.015128 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008203 \\ 0.008098 \\ 0.009909 \\ 0.009877 \\ 0.036087 \\ 0.019894 \\ 0.024787 \\ 0.024552 \\ 0.0118 \\ 0.011675 \\ 0.0095 \\ 0.009493 \\ 0.008703 \\ 0.008764 \\ 0.012854 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.00252 \\ -0.00252 \\ -0.002758 \\ -0.002758 \\ -0.003389 \\ -0.003659 \\ -0.003942 \\ -0.003942 \\ -0.004773 \\ -0.004773 \\ -0.005225 \\ -0.005225 \\ -0.005807 \\ -0.005807 \\ -0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ -0.01025 \\ 0.006821 \\ -0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ -0.006734 \\ 0.010485 \\ -0.010581 \\ 0.012967 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.497954 \\ -0.497954 \\ 0.499491 \\ -0.499491 \\ 0 \\ 0 \\ 0.001515 \\ -0.001515 \\ 0.001696 \\ -0.001696 \\ 0.499883 \\ -0.499883 \\ 0.501122 \\ -0.501122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.00256 \\ 0.002656 \\ -0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ -0.003033 \\ 0.003076 \\ -0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ 0.01025 \\ 0.006821 \\ 0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ 0.006734 \\ 0.010485 \\ 0.010581 \\ 0.012967 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.00256 \\ 0.002656 \\ 0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ 0.003033 \\ 0.003076 \\ 0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491e^{i0.149\pi} \\ 0.009491e^{i0.149\pi} \\ 0.010889e^{i0.135\pi} \\ 0.010889e^{i0.135\pi} \\ 0.005753 \\ 0.017147 \\ 0.035739e^{i0.334\pi} \\ 0.035739e^{i0.334\pi} \\ 0.018055e^{i0.326\pi} \\ 0.018055e^{i0.326\pi} \\ 0.038498e^{i0.377\pi} \\ 0.038498e^{i0.377\pi} \\ 0.030343e^{i0.369\pi} \\ 0.030343e^{i0.369\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491 \\ 0.009491 \\ 0.010889 \\ 0.010889 \\ 0.005753 \\ 0.017147 \\ 0.035739 \\ 0.035739 \\ 0.018055 \\ 0.018055 \\ 0.038498 \\ 0.038498 \\ 0.030343 \\ 0.030343 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.00499 \\ 0.007237 \\ 0.007237 \\ 0.00765 \\ 0.00765 \\ 0.008501 \\ 0.012277 \\ 0.01289 \\ 0.01289 \\ 0.013161 \\ 0.013161 \\ 0.015853 \\ 0.015853 \\ 0.017144 \\ 0.017144 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006817 \\ 0.008354 \\ 0.008529 \\ 0.009816 \\ 0.009946 \\ 0.005729 \\ 0.017042 \\ 0.016954 \\ 0.018308 \\ 0.009575 \\ 0.00904 \\ 0.014781 \\ 0.013893 \\ 0.012308 \\ 0.011771 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002501 \\ -0.003632 \\ -0.003632 \\ -0.00384 \\ -0.00384 \\ -0.004269 \\ -0.006176 \\ -0.006487 \\ -0.006487 \\ -0.006624 \\ -0.006624 \\ -0.00799 \\ -0.00799 \\ -0.008646 \\ -0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ -0.004353 \\ 0.004484 \\ -0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ -0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ -0.028072 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.503296 \\ -0.503296 \\ 0.502085 \\ -0.502085 \\ 0 \\ 0 \\ 0.512221 \\ -0.512221 \\ 0.009152 \\ -0.009152 \\ 0.009854 \\ -0.009854 \\ 0.492896 \\ -0.492896 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002709 \\ 0.002704 \\ -0.003165 \\ 0.003175 \\ 0 \\ 0 \\ -0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ -0.003598 \\ 0.004215 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ 0.004353 \\ 0.004484 \\ 0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ 0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ 0.028072 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002709 \\ 0.002704 \\ 0.003165 \\ 0.003175 \\ 0 \\ 0 \\ 0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ 0.003598 \\ 0.004215 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921e^{i0.147\pi} \\ 0.013921e^{i0.147\pi} \\ 0.020085e^{i0.333\pi} \\ 0.020085e^{i0.333\pi} \\ 0.02497e^{i0.247\pi} \\ 0.02497e^{i0.247\pi} \\ 0.006584e^{i0.249\pi} \\ 0.006584e^{i0.249\pi} \\ 0.042272 \\ 0.038761 \\ 0.038939e^{i0.081\pi} \\ 0.038939e^{i0.081\pi} \\ 0.01071e^{i0.226\pi} \\ 0.01071e^{i0.226\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921 \\ 0.013921 \\ 0.020085 \\ 0.020085 \\ 0.02497 \\ 0.02497 \\ 0.006584 \\ 0.006584 \\ 0.042272 \\ 0.038761 \\ 0.038939 \\ 0.038939 \\ 0.01071 \\ 0.01071 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.007462 \\ 0.008646 \\ 0.008646 \\ 0.009981 \\ 0.009981 \\ 0.011516 \\ 0.011516 \\ 0.011646 \\ 0.011646 \\ 0.013266 \\ 0.016435 \\ 0.018413 \\ 0.018413 \\ 0.01965 \\ 0.01965 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011366 \\ 0.012371 \\ 0.012443 \\ 0.010169 \\ 0.009863 \\ 0.018175 \\ 0.017302 \\ 0.004726 \\ 0.004549 \\ 0.04199 \\ 0.038441 \\ 0.036639 \\ 0.038033 \\ 0.008067 \\ 0.00803 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.003745 \\ -0.004342 \\ -0.004342 \\ -0.005016 \\ -0.005016 \\ -0.005791 \\ -0.005791 \\ -0.005857 \\ -0.005857 \\ -0.006677 \\ -0.008286 \\ -0.009293 \\ -0.009293 \\ -0.009923 \\ -0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ -0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ -0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ -0.009901 \\ 0.007071 \\ -0.007015 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.500922 \\ -0.500922 \\ 0.004855 \\ -0.004855 \\ 0.007834 \\ -0.007834 \\ 0.493908 \\ -0.493908 \\ 0 \\ 0 \\ 0.505942 \\ -0.505942 \\ 0.499257 \\ -0.499257 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ -0.001458 \\ 0.001529 \\ 0 \\ 0 \\ -0.01205 \\ 0.012172 \\ -0.00259 \\ 0.002637 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ 0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ 0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ 0.009901 \\ 0.007071 \\ 0.007015 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ 0.001458 \\ 0.001529 \\ 0 \\ 0 \\ 0.01205 \\ 0.012172 \\ 0.00259 \\ 0.002637 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552e^{i0.352\pi} \\ 0.016552e^{i0.352\pi} \\ 0.009933e^{i0.202\pi} \\ 0.009933e^{i0.202\pi} \\ 0.016999e^{i0.132\pi} \\ 0.016999e^{i0.132\pi} \\ 0.023078 \\ 0.004973e^{i0.076\pi} \\ 0.004973e^{i0.076\pi} \\ 0.03488e^{i0.248\pi} \\ 0.03488e^{i0.248\pi} \\ 0.030281e^{i0.308\pi} \\ 0.030281e^{i0.308\pi} \\ 0.044571e^{i0.343\pi} \\ 0.044571e^{i0.343\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552 \\ 0.016552 \\ 0.009933 \\ 0.009933 \\ 0.016999 \\ 0.016999 \\ 0.023078 \\ 0.004973 \\ 0.004973 \\ 0.03488 \\ 0.03488 \\ 0.030281 \\ 0.030281 \\ 0.044571 \\ 0.044571 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.008942 \\ 0.008942 \\ 0.009021 \\ 0.009021 \\ 0.01347 \\ 0.01347 \\ 0.017582 \\ 0.024138 \\ 0.024138 \\ 0.025482 \\ 0.025482 \\ 0.031633 \\ 0.031633 \\ 0.0339 \\ 0.0339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007401 \\ 0.007394 \\ 0.007934 \\ 0.007984 \\ 0.015354 \\ 0.015539 \\ 0.022874 \\ 0.004981 \\ 0.00456 \\ 0.023357 \\ 0.025604 \\ 0.017488 \\ 0.016354 \\ 0.021451 \\ 0.019999 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.004491 \\ -0.004491 \\ -0.004531 \\ -0.004531 \\ -0.006781 \\ -0.006781 \\ -0.008869 \\ -0.012217 \\ -0.012217 \\ -0.012906 \\ -0.012906 \\ -0.016072 \\ -0.016072 \\ -0.017244 \\ -0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ -0.005932 \\ 0.006915 \\ -0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ -0.025988 \\ 0.025696 \\ -0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000148 \\ -0.000148 \\ 0.501012 \\ -0.501012 \\ 0.501897 \\ -0.501897 \\ 0 \\ 0.014014 \\ -0.014014 \\ 0.514598 \\ -0.514598 \\ 0.489335 \\ -0.489335 \\ 0.011148 \\ -0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ -0.002547 \\ 0.002566 \\ -0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ -0.008163 \\ 0.007836 \\ -0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ 0.005932 \\ 0.006915 \\ 0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ 0.025988 \\ 0.025696 \\ 0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ 0.002547 \\ 0.002566 \\ 0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ 0.008163 \\ 0.007836 \\ 0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165e^{i0.337\pi} \\ 0.057165e^{i0.337\pi} \\ 0.016817e^{i0.290\pi} \\ 0.016817e^{i0.290\pi} \\ 0.025934e^{i0.183\pi} \\ 0.025934e^{i0.183\pi} \\ 0.045487e^{i0.269\pi} \\ 0.045487e^{i0.269\pi} \\ 0.073076e^{i0.319\pi} \\ 0.073076e^{i0.319\pi} \\ 0.026551e^{i0.378\pi} \\ 0.026551e^{i0.378\pi} \\ 0.021225e^{i0.085\pi} \\ 0.021225e^{i0.085\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165 \\ 0.057165 \\ 0.016817 \\ 0.016817 \\ 0.025934 \\ 0.025934 \\ 0.045487 \\ 0.045487 \\ 0.073076 \\ 0.073076 \\ 0.026551 \\ 0.026551 \\ 0.021225 \\ 0.021225 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.00775 \\ 0.032161 \\ 0.032161 \\ 0.03321 \\ 0.03321 \\ 0.041272 \\ 0.041272 \\ 0.047259 \\ 0.047259 \\ 0.055642 \\ 0.055642 \\ 0.057218 \\ 0.057218 \\ 0.08291 \\ 0.08291 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001584 \\ 0.028407 \\ 0.026784 \\ 0.00958 \\ 0.01065 \\ 0.021377 \\ 0.021259 \\ 0.03091 \\ 0.027901 \\ 0.039117 \\ 0.037439 \\ 0.009404 \\ 0.009809 \\ 0.018044 \\ 0.021054 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.00389 \\ -0.016345 \\ -0.016345 \\ -0.016887 \\ -0.016887 \\ -0.021074 \\ -0.021074 \\ -0.024206 \\ -0.024206 \\ -0.028625 \\ -0.028625 \\ -0.02946 \\ -0.02946 \\ -0.043275 \\ -0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ -0.009696 \\ -0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ -0.009368 \\ -0.010459 \\ -0.021059 \\ -0.021996 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ -0.009356 \\ 0.98319 \\ -0.98319 \\ 0.000884 \\ -0.000884 \\ 0.016277 \\ -0.016277 \\ 0.006976 \\ -0.006976 \\ 0.99329 \\ -0.99329 \\ 0.975543 \\ -0.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ -0.004517 \\ -0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ -0.008221 \\ 1.991908 \\ -0.002428 \\ -0.001362 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ 0.009696 \\ 0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ 0.009368 \\ 0.010459 \\ 0.021059 \\ 0.021996 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ 0.004517 \\ 0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ 0.008221 \\ 1.991908 \\ 0.002428 \\ 0.001362 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | $ \begin{pmatrix} 1 \\ 0.993372 \\ 0.992175e^{i0.672\pi} \\ 0.992175e^{-i0.672\pi} \\ 0.989373 \\ 0.987761e^{i0.672\pi} \\ 0.987761e^{-i0.672\pi} \\ 0.986442 \\ 0.982177e^{i0.022\pi} \\ 0.982177e^{-i0.022\pi} \\ 0.978777e^{i0.695\pi} \\ 0.978777e^{-i0.695\pi} \\ 0.977417e^{i0.650\pi} \\ 0.977417e^{-i0.650\pi} \\ 0.975866e^{i0.023\pi} \\ 0.975866e^{-i0.023\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017752 \\ 0.023302e^{i0.232\pi} \\ 0.023302e^{i0.232\pi} \\ 0.008184 \\ 0.028139e^{i0.265\pi} \\ 0.028139e^{i0.265\pi} \\ 0.023689 \\ 0.035428e^{i0.307\pi} \\ 0.035428e^{i0.307\pi} \\ 0.066361e^{i0.302\pi} \\ 0.066361e^{i0.302\pi} \\ 0.063601e^{i0.287\pi} \\ 0.063601e^{i0.287\pi} \\ 0.046033e^{i0.276\pi} \\ 0.046033e^{i0.276\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.992537 \\ 0.991889e^{i0.669\pi} \\ 0.991889e^{-i0.669\pi} \\ 0.990745 \\ 0.987882e^{i0.669\pi} \\ 0.987882e^{-i0.669\pi} \\ 0.987304 \\ 0.977682e^{i0.021\pi} \\ 0.977682e^{-i0.021\pi} \\ 0.979422e^{i0.691\pi} \\ 0.979422e^{-i0.691\pi} \\ 0.97645e^{i0.647\pi} \\ 0.97645e^{-i0.647\pi} \\ 0.980146e^{i0.023\pi} \\ 0.980146e^{-i0.023\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000835 \\ 0.011215 \\ 0.011215 \\ 0.001371 \\ 0.008351 \\ 0.008351 \\ 0.000862 \\ 0.004906 \\ 0.004906 \\ 0.010227 \\ 0.010227 \\ 0.009968 \\ 0.009968 \\ 0.004291 \\ 0.004291 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017752 \\ 0.023302 \\ 0.023302 \\ 0.008184 \\ 0.028139 \\ 0.028139 \\ 0.023689 \\ 0.035428 \\ 0.035428 \\ 0.066361 \\ 0.066361 \\ 0.063601 \\ 0.063601 \\ 0.046033 \\ 0.046033 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.014042 \\ 0.015935 \\ 0.015935 \\ 0.019783 \\ 0.024243 \\ 0.024243 \\ 0.026082 \\ 0.039745 \\ 0.039745 \\ 0.041416 \\ 0.041416 \\ 0.04565 \\ 0.04565 \\ 0.043509 \\ 0.043509 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017619 \\ 0.006163 \\ 0.02362 \\ 0.008108 \\ 0.006642 \\ 0.025649 \\ 0.023388 \\ 0.020995 \\ 0.018359 \\ 0.00983 \\ 0.052727 \\ 0.017269 \\ 0.051625 \\ 0.03122 \\ 0.026996 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.00665 \\ -0.007856 \\ -0.007856 \\ -0.010683 \\ -0.012315 \\ -0.012315 \\ -0.013651 \\ -0.017984 \\ -0.017984 \\ -0.021451 \\ -0.021451 \\ -0.022842 \\ -0.022842 \\ -0.02443 \\ -0.02443 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017712 \\ 0.0046 \\ -0.022654 \\ 0.008238 \\ 0.0085 \\ -0.028305 \\ 0.023731 \\ 0.022659 \\ 0.018743 \\ 0.024079 \\ -0.070203 \\ 0.028395 \\ -0.065864 \\ 0.033022 \\ 0.028146 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.672353 \\ -0.672353 \\ 0 \\ 0.672032 \\ -0.672032 \\ 0 \\ 0.021925 \\ -0.021925 \\ 0.69465 \\ -0.69465 \\ 0.650477 \\ -0.650477 \\ 0.022951 \\ -0.022951 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.007314 \\ 0.002273 \\ 0 \\ -0.008615 \\ 0.001845 \\ 0 \\ 0.008767 \\ 0.009685 \\ -0.019901 \\ 0.000267 \\ -0.018314 \\ 0.004304 \\ 0.010375 \\ 0.011787 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000841 \\ 0.000289 \\ 0.000289 \\ 0.001385 \\ 0.000123 \\ 0.000123 \\ 0.000874 \\ 0.004587 \\ 0.004587 \\ 0.000658 \\ 0.000658 \\ 0.000991 \\ 0.000991 \\ 0.004376 \\ 0.004376 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017712 \\ 0.0046 \\ 0.022654 \\ 0.008238 \\ 0.0085 \\ 0.028305 \\ 0.023731 \\ 0.022659 \\ 0.018743 \\ 0.024079 \\ 0.070203 \\ 0.028395 \\ 0.065864 \\ 0.033022 \\ 0.028146 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.003597 \\ 0.003597 \\ 0 \\ 0.002691 \\ 0.002691 \\ 0 \\ 0.000638 \\ 0.000638 \\ 0.003318 \\ 0.003318 \\ 0.003232 \\ 0.003232 \\ 0.000101 \\ 0.000101 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.007314 \\ 0.002273 \\ 0 \\ 0.008615 \\ 0.001845 \\ 0 \\ 0.008767 \\ 0.009685 \\ 0.019901 \\ 0.000267 \\ 0.018314 \\ 0.004304 \\ 0.010375 \\ 0.011787 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.99239 \\ 0.991821e^{i0.669\pi} \\ 0.991821e^{-i0.669\pi} \\ 0.991379e^{i0.009\pi} \\ 0.991379e^{-i0.009\pi} \\ 0.990616 \\ 0.988792e^{i0.660\pi} \\ 0.988792e^{-i0.660\pi} \\ 0.988008e^{i0.002\pi} \\ 0.988008e^{-i0.002\pi} \\ 0.987666e^{i0.663\pi} \\ 0.987666e^{-i0.663\pi} \\ 0.986517e^{i0.673\pi} \\ 0.986517e^{-i0.673\pi} \\ 0.985684 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02826 \\ 0.027822e^{i0.029\pi} \\ 0.027822e^{i0.029\pi} \\ 0.036253e^{i0.265\pi} \\ 0.036253e^{i0.265\pi} \\ 0.022415 \\ 0.056784e^{i0.344\pi} \\ 0.056784e^{i0.344\pi} \\ 0.033516e^{i0.208\pi} \\ 0.033516e^{i0.208\pi} \\ 0.032837e^{i0.222\pi} \\ 0.032837e^{i0.222\pi} \\ 0.068819e^{i0.110\pi} \\ 0.068819e^{i0.110\pi} \\ 0.049819 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.991675 \\ 0.991518e^{i0.667\pi} \\ 0.991518e^{-i0.667\pi} \\ 0.990041e^{i0.007\pi} \\ 0.990041e^{-i0.007\pi} \\ 0.990658 \\ 0.988753e^{i0.660\pi} \\ 0.988753e^{-i0.660\pi} \\ 0.989426e^{i0.005\pi} \\ 0.989426e^{-i0.005\pi} \\ 0.986856e^{i0.666\pi} \\ 0.986856e^{-i0.666\pi} \\ 0.987251e^{i0.673\pi} \\ 0.987251e^{-i0.673\pi} \\ 0.98702 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000715 \\ 0.006861 \\ 0.006861 \\ 0.007367 \\ 0.007367 \\ 0.000042 \\ 0.0012 \\ 0.0012 \\ 0.008852 \\ 0.008852 \\ 0.008144 \\ 0.008144 \\ 0.000734 \\ 0.000734 \\ 0.001336 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02826 \\ 0.027822 \\ 0.027822 \\ 0.036253 \\ 0.036253 \\ 0.022415 \\ 0.056784 \\ 0.056784 \\ 0.033516 \\ 0.033516 \\ 0.032837 \\ 0.032837 \\ 0.068819 \\ 0.068819 \\ 0.049819 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.015871 \\ 0.016615 \\ 0.016615 \\ 0.018521 \\ 0.018521 \\ 0.018638 \\ 0.022329 \\ 0.022329 \\ 0.022477 \\ 0.022477 \\ 0.025349 \\ 0.025349 \\ 0.02606 \\ 0.02606 \\ 0.02711 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028025 \\ 0.010028 \\ 0.037538 \\ 0.024666 \\ 0.02359 \\ 0.022206 \\ 0.010394 \\ 0.035877 \\ 0.026745 \\ 0.025904 \\ 0.009172 \\ 0.033955 \\ 0.021753 \\ 0.087725 \\ 0.049172 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.007639 \\ -0.008213 \\ -0.008213 \\ -0.008659 \\ -0.008659 \\ -0.009428 \\ -0.011271 \\ -0.011271 \\ -0.012064 \\ -0.012064 \\ -0.01241 \\ -0.01241 \\ -0.013575 \\ -0.013575 \\ -0.014419 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028079 \\ -0.01172 \\ -0.016197 \\ 0.025392 \\ 0.023867 \\ 0.022375 \\ 0.032017 \\ -0.059137 \\ 0.026917 \\ 0.026637 \\ 0.006545 \\ -0.031517 \\ -0.011286 \\ -0.054588 \\ 0.049306 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.669102 \\ -0.669102 \\ 0.009423 \\ -0.009423 \\ 0 \\ 0.659855 \\ -0.659855 \\ 0.002276 \\ -0.002276 \\ 0.663406 \\ -0.663406 \\ 0.672638 \\ -0.672638 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00817 \\ 0.007379 \\ 0.008171 \\ 0.008636 \\ 0 \\ -0.014825 \\ -0.000241 \\ 0.006332 \\ 0.006453 \\ -0.010341 \\ 0.003863 \\ -0.022044 \\ 0.014791 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000721 \\ 0.000305 \\ 0.000305 \\ 0.00135 \\ 0.00135 \\ 0.000042 \\ 0.000039 \\ 0.000039 \\ 0.001435 \\ 0.001435 \\ 0.000821 \\ 0.000821 \\ 0.000744 \\ 0.000744 \\ 0.001355 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028079 \\ 0.01172 \\ 0.016197 \\ 0.025392 \\ 0.023867 \\ 0.022375 \\ 0.032017 \\ 0.059137 \\ 0.026917 \\ 0.026637 \\ 0.006545 \\ 0.031517 \\ 0.011286 \\ 0.054588 \\ 0.049306 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.0022 \\ 0.0022 \\ 0.002328 \\ 0.002328 \\ 0 \\ 0.000386 \\ 0.000386 \\ 0.002813 \\ 0.002813 \\ 0.002613 \\ 0.002613 \\ 0.000007 \\ 0.000007 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00817 \\ 0.007379 \\ 0.008171 \\ 0.008636 \\ 0 \\ 0.014825 \\ 0.000241 \\ 0.006332 \\ 0.006453 \\ 0.010341 \\ 0.003863 \\ 0.022044 \\ 0.014791 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | $ \begin{pmatrix} 1 \\ 0.991701 \\ 0.988421e^{i0.992\pi} \\ 0.988421e^{-i0.992\pi} \\ 0.986273 \\ 0.982149e^{i0.992\pi} \\ 0.982149e^{-i0.992\pi} \\ 0.98101 \\ 0.974075e^{i0.031\pi} \\ 0.974075e^{-i0.031\pi} \\ 0.970885e^{i0.961\pi} \\ 0.970885e^{-i0.961\pi} \\ 0.970547e^{i0.976\pi} \\ 0.970547e^{-i0.976\pi} \\ 0.970417e^{i0.033\pi} \\ 0.970417e^{-i0.033\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013675 \\ 0.031312e^{i0.321\pi} \\ 0.031312e^{i0.321\pi} \\ 0.015026 \\ 0.035396e^{i0.317\pi} \\ 0.035396e^{i0.317\pi} \\ 0.023035 \\ 0.058434e^{i0.359\pi} \\ 0.058434e^{i0.359\pi} \\ 0.112596e^{i0.149\pi} \\ 0.112596e^{i0.149\pi} \\ 0.077277e^{i0.142\pi} \\ 0.077277e^{i0.142\pi} \\ 0.061884e^{i0.287\pi} \\ 0.061884e^{i0.287\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.990018 \\ 0.988425e^{i0.997\pi} \\ 0.988425e^{-i0.997\pi} \\ 0.986591 \\ 0.983148e^{i0.996\pi} \\ 0.983148e^{-i0.996\pi} \\ 0.982082 \\ 0.973274e^{i0.031\pi} \\ 0.973274e^{-i0.031\pi} \\ 0.971802e^{i0.965\pi} \\ 0.971802e^{-i0.965\pi} \\ 0.96913e^{i0.972\pi} \\ 0.96913e^{-i0.972\pi} \\ 0.970865e^{i0.032\pi} \\ 0.970865e^{-i0.032\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001683 \\ 0.01304 \\ 0.01304 \\ 0.000318 \\ 0.01068 \\ 0.01068 \\ 0.001072 \\ 0.002149 \\ 0.002149 \\ 0.012612 \\ 0.012612 \\ 0.011952 \\ 0.011952 \\ 0.004022 \\ 0.004022 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013675 \\ 0.031312 \\ 0.031312 \\ 0.015026 \\ 0.035396 \\ 0.035396 \\ 0.023035 \\ 0.058434 \\ 0.058434 \\ 0.112596 \\ 0.112596 \\ 0.077277 \\ 0.077277 \\ 0.061884 \\ 0.061884 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.018198 \\ 0.023105 \\ 0.023105 \\ 0.026952 \\ 0.034458 \\ 0.034458 \\ 0.036568 \\ 0.05196 \\ 0.05196 \\ 0.056571 \\ 0.056571 \\ 0.059484 \\ 0.059484 \\ 0.057864 \\ 0.057864 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013539 \\ 0.016345 \\ 0.016708 \\ 0.014825 \\ 0.018669 \\ 0.019153 \\ 0.022622 \\ 0.026723 \\ 0.021905 \\ 0.086246 \\ 0.107811 \\ 0.061385 \\ 0.073244 \\ 0.040878 \\ 0.033377 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.008334 \\ -0.011646 \\ -0.011646 \\ -0.013822 \\ -0.018012 \\ -0.018012 \\ -0.019173 \\ -0.026267 \\ -0.026267 \\ -0.029547 \\ -0.029547 \\ -0.029896 \\ -0.029896 \\ -0.030029 \\ -0.030029 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013695 \\ -0.016017 \\ -0.017355 \\ 0.01512 \\ -0.018557 \\ -0.020042 \\ 0.023209 \\ 0.031658 \\ 0.02174 \\ -0.098613 \\ -0.1146 \\ -0.070638 \\ -0.076648 \\ 0.044602 \\ 0.034946 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.992312 \\ -0.992312 \\ 0 \\ 0.992484 \\ -0.992484 \\ 0 \\ 0.030785 \\ -0.030785 \\ 0.960648 \\ -0.960648 \\ 0.975929 \\ -0.975929 \\ 0.033357 \\ -0.033357 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.008794 \\ 1.991459 \\ 0 \\ -0.009959 \\ 1.990327 \\ 0 \\ 0.015867 \\ 0.017578 \\ -0.022761 \\ -0.014004 \\ -0.013551 \\ -0.009899 \\ 0.013874 \\ 0.016559 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001699 \\ 0.000004 \\ 0.000004 \\ 0.000322 \\ 0.001017 \\ 0.001017 \\ 0.001093 \\ 0.000823 \\ 0.000823 \\ 0.000944 \\ 0.000944 \\ 0.001461 \\ 0.001461 \\ 0.000461 \\ 0.000461 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013695 \\ 0.016017 \\ 0.017355 \\ 0.01512 \\ 0.018557 \\ 0.020042 \\ 0.023209 \\ 0.031658 \\ 0.02174 \\ 0.098613 \\ 0.1146 \\ 0.070638 \\ 0.076648 \\ 0.044602 \\ 0.034946 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.0042 \\ 0.0042 \\ 0 \\ 0.003444 \\ 0.003444 \\ 0 \\ 0.000652 \\ 0.000652 \\ 0.004122 \\ 0.004122 \\ 0.003895 \\ 0.003895 \\ 0.001311 \\ 0.001311 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.008794 \\ 1.991459 \\ 0 \\ 0.009959 \\ 1.990327 \\ 0 \\ 0.015867 \\ 0.017578 \\ 0.022761 \\ 0.014004 \\ 0.013551 \\ 0.009899 \\ 0.013874 \\ 0.016559 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.989569 \\ 0.989362e^{i0.998\pi} \\ 0.989362e^{-i0.998\pi} \\ 0.988521e^{i0.009\pi} \\ 0.988521e^{-i0.009\pi} \\ 0.987493 \\ 0.985434e^{i0.993\pi} \\ 0.985434e^{-i0.993\pi} \\ 0.982696e^{i0.004\pi} \\ 0.982696e^{-i0.004\pi} \\ 0.981781e^{i0.997\pi} \\ 0.981781e^{-i0.997\pi} \\ 0.980289e^{i0.994\pi} \\ 0.980289e^{-i0.994\pi} \\ 0.980011 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036346 \\ 0.026566e^{i0.310\pi} \\ 0.026566e^{i0.310\pi} \\ 0.042282e^{i0.233\pi} \\ 0.042282e^{i0.233\pi} \\ 0.017259 \\ 0.065153e^{i0.171\pi} \\ 0.065153e^{i0.171\pi} \\ 0.045267e^{i0.408\pi} \\ 0.045267e^{i0.408\pi} \\ 0.038194e^{i0.372\pi} \\ 0.038194e^{i0.372\pi} \\ 0.105627e^{i0.286\pi} \\ 0.105627e^{i0.286\pi} \\ 0.023971 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.988218 \\ 0.987942e^{i0.999\pi} \\ 0.987942e^{-i0.999\pi} \\ 0.988371e^{i0.006\pi} \\ 0.988371e^{-i0.006\pi} \\ 0.986835 \\ 0.984504e^{i0.993\pi} \\ 0.984504e^{-i0.993\pi} \\ 0.981678e^{i0.007\pi} \\ 0.981678e^{-i0.007\pi} \\ -0.982095 \\ -0.984331 \\ 0.98255e^{i0.994\pi} \\ 0.98255e^{-i0.994\pi} \\ 0.981631 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001351 \\ 0.003303 \\ 0.003303 \\ 0.008859 \\ 0.008859 \\ 0.000658 \\ 0.001943 \\ 0.001943 \\ 0.008278 \\ 0.008278 \\ 0.010084 \\ 0.010407 \\ 0.002267 \\ 0.002267 \\ 0.00162 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036346 \\ 0.026566 \\ 0.026566 \\ 0.042282 \\ 0.042282 \\ 0.017259 \\ 0.065153 \\ 0.065153 \\ 0.045267 \\ 0.045267 \\ 0.038194 \\ 0.038194 \\ 0.105627 \\ 0.105627 \\ 0.023971 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.022089 \\ 0.022572 \\ 0.022572 \\ 0.023013 \\ 0.023013 \\ 0.025508 \\ 0.029838 \\ 0.029838 \\ 0.035342 \\ 0.035342 \\ 0.035849 \\ 0.033654 \\ 0.036817 \\ 0.036817 \\ 0.037991 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.035918 \\ 0.014712 \\ 0.014768 \\ 0.031676 \\ 0.030446 \\ 0.017032 \\ 0.053886 \\ 0.05628 \\ 0.012931 \\ 0.012398 \\ 0.014641 \\ 0.014674 \\ 0.063369 \\ 0.065958 \\ 0.023531 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.010485 \\ -0.010695 \\ -0.010695 \\ -0.011545 \\ -0.011545 \\ -0.012586 \\ -0.014673 \\ -0.014673 \\ -0.017455 \\ -0.017455 \\ -0.018387 \\ -0.018387 \\ -0.019907 \\ -0.019907 \\ -0.020192 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036071 \\ -0.014828 \\ -0.015053 \\ 0.032446 \\ 0.030902 \\ 0.017327 \\ -0.056914 \\ -0.058698 \\ 0.014538 \\ 0.013447 \\ -0.014261 \\ -0.015018 \\ -0.063529 \\ -0.06734 \\ 0.024166 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.99844 \\ -0.99844 \\ 0.009153 \\ -0.009153 \\ 0 \\ 0.992531 \\ -0.992531 \\ 0.004044 \\ -0.004044 \\ 0.996733 \\ -0.996733 \\ 0.993685 \\ -0.993685 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.007202 \\ 1.992844 \\ 0.008531 \\ 0.009109 \\ 0 \\ -0.011856 \\ 1.989023 \\ 0.013802 \\ 0.013922 \\ -0.011617 \\ 1.988475 \\ -0.02907 \\ 1.97173 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001366 \\ 0.001437 \\ 0.001437 \\ 0.000152 \\ 0.000152 \\ 0.000667 \\ 0.000944 \\ 0.000944 \\ 0.001037 \\ 0.001037 \\ 0.00032 \\ 0.002594 \\ 0.002303 \\ 0.002303 \\ 0.001652 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036071 \\ 0.014828 \\ 0.015053 \\ 0.032446 \\ 0.030902 \\ 0.017327 \\ 0.056914 \\ 0.058698 \\ 0.014538 \\ 0.013447 \\ 0.014261 \\ 0.015018 \\ 0.063529 \\ 0.06734 \\ 0.024166 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.00096 \\ 0.00096 \\ 0.002853 \\ 0.002853 \\ 0 \\ 0.000551 \\ 0.000551 \\ 0.002663 \\ 0.002663 \\ 0.003267 \\ 1.996733 \\ 0.000056 \\ 0.000056 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.007202 \\ 1.992844 \\ 0.008531 \\ 0.009109 \\ 0 \\ 0.011856 \\ 1.989023 \\ 0.013802 \\ 0.013922 \\ 0.011617 \\ 1.988475 \\ 0.02907 \\ 1.97173 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | $ \begin{pmatrix} 1 \\ 0.980029e^{i0.000\pi} \\ 0.980029e^{-i0.000\pi} \\ 0.970739e^{i0.661\pi} \\ 0.970739e^{-i0.661\pi} \\ 0.965594e^{i0.850\pi} \\ 0.965594e^{-i0.850\pi} \\ 0.96355e^{i0.153\pi} \\ 0.96355e^{-i0.153\pi} \\ 0.962948e^{i0.492\pi} \\ 0.962948e^{-i0.492\pi} \\ 0.960081e^{i0.644\pi} \\ 0.960081e^{-i0.644\pi} \\ 0.959069 \\ 0.958535e^{i0.505\pi} \\ 0.958535e^{-i0.505\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.059365e^{i0.442\pi} \\ 0.059365e^{i0.442\pi} \\ 0.023564e^{i0.315\pi} \\ 0.023564e^{i0.315\pi} \\ 0.06433e^{i0.244\pi} \\ 0.06433e^{i0.244\pi} \\ 0.086548e^{i0.279\pi} \\ 0.086548e^{i0.279\pi} \\ 0.0664e^{i0.180\pi} \\ 0.0664e^{i0.180\pi} \\ 0.032125e^{i0.242\pi} \\ 0.032125e^{i0.242\pi} \\ 0.029432 \\ 0.041859e^{i0.233\pi} \\ 0.041859e^{i0.233\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.975902 \\ 0.982908 \\ 0.971652e^{i0.660\pi} \\ 0.971652e^{-i0.660\pi} \\ 0.966004e^{i0.846\pi} \\ 0.966004e^{-i0.846\pi} \\ 0.964439e^{i0.158\pi} \\ 0.964439e^{-i0.158\pi} \\ 0.964237e^{i0.497\pi} \\ 0.964237e^{-i0.497\pi} \\ 0.959907e^{i0.653\pi} \\ 0.959907e^{-i0.653\pi} \\ 0.957884 \\ 0.956447e^{i0.501\pi} \\ 0.956447e^{-i0.501\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004325 \\ 0.003159 \\ 0.002446 \\ 0.002446 \\ 0.013589 \\ 0.013589 \\ 0.014908 \\ 0.014908 \\ 0.014689 \\ 0.014689 \\ 0.02662 \\ 0.02662 \\ 0.001185 \\ 0.012833 \\ 0.012833 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.059365 \\ 0.059365 \\ 0.023564 \\ 0.023564 \\ 0.06433 \\ 0.06433 \\ 0.086548 \\ 0.086548 \\ 0.0664 \\ 0.0664 \\ 0.032125 \\ 0.032125 \\ 0.029432 \\ 0.041859 \\ 0.041859 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.043589 \\ 0.036723 \\ 0.056781 \\ 0.056781 \\ 0.067324 \\ 0.067324 \\ 0.070825 \\ 0.070825 \\ 0.071597 \\ 0.071597 \\ 0.078766 \\ 0.078766 \\ 0.081323 \\ 0.083292 \\ 0.083292 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010528 \\ 0.010604 \\ 0.004964 \\ 0.017108 \\ 0.018819 \\ 0.060539 \\ 0.072396 \\ 0.021456 \\ 0.054585 \\ 0.053437 \\ 0.009521 \\ 0.030168 \\ 0.028193 \\ 0.029765 \\ 0.029865 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.020174 \\ -0.020174 \\ -0.029697 \\ -0.029697 \\ -0.035011 \\ -0.035011 \\ -0.037131 \\ -0.037131 \\ -0.037755 \\ -0.037755 \\ -0.040737 \\ -0.040737 \\ -0.041792 \\ -0.042349 \\ -0.042349 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.012758 \\ 0.012604 \\ 0.011435 \\ -0.024497 \\ -0.020136 \\ -0.065651 \\ 0.08016 \\ 0.022442 \\ 0.039303 \\ -0.03428 \\ 0.010566 \\ -0.031746 \\ 0.030227 \\ 0.028766 \\ -0.029528 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000422 \\ -0.000422 \\ 0.660847 \\ -0.660847 \\ 0.85041 \\ -0.85041 \\ 0.153375 \\ -0.153375 \\ 0.491783 \\ -0.491783 \\ 0.643858 \\ -0.643858 \\ 0 \\ 0.504748 \\ -0.504748 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018726 \\ 0.018738 \\ -0.006766 \\ 0.000611 \\ -0.020443 \\ -0.006586 \\ 0.010154 \\ 0.027363 \\ -0.017514 \\ 0.019483 \\ -0.010047 \\ 0.00387 \\ 0 \\ -0.010193 \\ 0.01052 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.00422 \\ 0.002934 \\ 0.00094 \\ 0.00094 \\ 0.000424 \\ 0.000424 \\ 0.000923 \\ 0.000923 \\ 0.001337 \\ 0.001337 \\ 0.000182 \\ 0.000182 \\ 0.001237 \\ 0.002181 \\ 0.002181 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.012758 \\ 0.012604 \\ 0.011435 \\ 0.024497 \\ 0.020136 \\ 0.065651 \\ 0.08016 \\ 0.022442 \\ 0.039303 \\ 0.03428 \\ 0.010566 \\ 0.031746 \\ 0.030227 \\ 0.028766 \\ 0.029528 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000422 \\ 0.000422 \\ 0.000744 \\ 0.000744 \\ 0.004477 \\ 0.004477 \\ 0.004914 \\ 0.004914 \\ 0.004834 \\ 0.004834 \\ 0.008827 \\ 0.008827 \\ 0 \\ 0.00421 \\ 0.00421 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018726 \\ 0.018738 \\ 0.006766 \\ 0.000611 \\ 0.020443 \\ 0.006586 \\ 0.010154 \\ 0.027363 \\ 0.017514 \\ 0.019483 \\ 0.010047 \\ 0.00387 \\ 0 \\ 0.010193 \\ 0.01052 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | $ \begin{pmatrix} 1 \\ -0.976304 \\ -0.964205 \\ 0.963423e^{i0.490\pi} \\ 0.963423e^{-i0.490\pi} \\ 0.961888e^{i0.508\pi} \\ 0.961888e^{-i0.508\pi} \\ 0.961633 \\ 0.958608e^{i0.996\pi} \\ 0.958608e^{-i0.996\pi} \\ 0.958365e^{i0.515\pi} \\ 0.958365e^{-i0.515\pi} \\ 0.958313e^{i0.486\pi} \\ 0.958313e^{-i0.486\pi} \\ 0.952865e^{i0.002\pi} \\ 0.952865e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044964 \\ 0.199082 \\ 0.055404e^{i0.217\pi} \\ 0.055404e^{i0.217\pi} \\ 0.069971e^{i0.377\pi} \\ 0.069971e^{i0.377\pi} \\ 0.06657 \\ 0.066479e^{i0.093\pi} \\ 0.066479e^{i0.093\pi} \\ 0.049845e^{i0.203\pi} \\ 0.049845e^{i0.203\pi} \\ 0.081144e^{i0.243\pi} \\ 0.081144e^{i0.243\pi} \\ 0.07755e^{i0.249\pi} \\ 0.07755e^{i0.249\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -0.981494 \\ -0.959108 \\ 0.958809e^{i0.488\pi} \\ 0.958809e^{-i0.488\pi} \\ 0.96412e^{i0.512\pi} \\ 0.96412e^{-i0.512\pi} \\ 0.954803 \\ 0.957082e^{i0.998\pi} \\ 0.957082e^{-i0.998\pi} \\ 0.957597e^{i0.513\pi} \\ 0.957597e^{-i0.513\pi} \\ 0.963278e^{i0.486\pi} \\ 0.963278e^{-i0.486\pi} \\ 0.95599e^{i0.002\pi} \\ 0.95599e^{-i0.002\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.00519 \\ 0.005097 \\ 0.007459 \\ 0.007459 \\ 0.011764 \\ 0.011764 \\ 0.00683 \\ 0.007179 \\ 0.007179 \\ 0.004728 \\ 0.004728 \\ 0.005371 \\ 0.005371 \\ 0.003334 \\ 0.003334 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044964 \\ 0.199082 \\ 0.055404 \\ 0.055404 \\ 0.069971 \\ 0.069971 \\ 0.06657 \\ 0.066479 \\ 0.066479 \\ 0.049845 \\ 0.049845 \\ 0.081144 \\ 0.081144 \\ 0.07755 \\ 0.07755 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.041764 \\ 0.075223 \\ 0.076279 \\ 0.076279 \\ 0.072692 \\ 0.072692 \\ 0.081829 \\ 0.082558 \\ 0.082558 \\ 0.082283 \\ 0.082283 \\ 0.07688 \\ 0.07688 \\ 0.089071 \\ 0.089071 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044132 \\ 0.190941 \\ 0.042716 \\ 0.039719 \\ 0.024503 \\ 0.026476 \\ 0.063561 \\ 0.060574 \\ 0.061336 \\ 0.036703 \\ 0.039908 \\ 0.059008 \\ 0.053938 \\ 0.052847 \\ 0.052263 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.023981 \\ -0.036451 \\ -0.037263 \\ -0.037263 \\ -0.038857 \\ -0.038857 \\ -0.039122 \\ -0.042273 \\ -0.042273 \\ -0.042527 \\ -0.042527 \\ -0.042581 \\ -0.042581 \\ -0.048282 \\ -0.048282 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.04715 \\ -0.231267 \\ 0.037767 \\ -0.034377 \\ 0.064839 \\ -0.070099 \\ 0.066935 \\ -0.068207 \\ -0.068826 \\ 0.029465 \\ -0.032583 \\ 0.060777 \\ -0.055157 \\ 0.057907 \\ 0.057214 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 1 \\ 1 \\ 0.49037 \\ -0.49037 \\ 0.508491 \\ -0.508491 \\ 0 \\ 0.995678 \\ -0.995678 \\ 0.51486 \\ -0.51486 \\ 0.4864 \\ -0.4864 \\ 0.002156 \\ -0.002156 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.013347 \\ 0.01507 \\ -0.00874 \\ 0.008776 \\ 0 \\ -0.007081 \\ 1.99353 \\ -0.013348 \\ 0.013252 \\ -0.017587 \\ 0.021435 \\ 0.017134 \\ 0.017381 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.005302 \\ 0.0053 \\ 0.004801 \\ 0.004801 \\ 0.002318 \\ 0.002318 \\ 0.007128 \\ 0.001593 \\ 0.001593 \\ 0.000802 \\ 0.000802 \\ 0.005168 \\ 0.005168 \\ 0.003274 \\ 0.003274 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04715 \\ 0.231267 \\ 0.037767 \\ 0.034377 \\ 0.064839 \\ 0.070099 \\ 0.066935 \\ 0.068207 \\ 0.068826 \\ 0.029465 \\ 0.032583 \\ 0.060777 \\ 0.055157 \\ 0.057907 \\ 0.057214 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.001941 \\ 0.001941 \\ 0.003818 \\ 0.003818 \\ 0 \\ 0.002331 \\ 0.002331 \\ 0.00155 \\ 0.00155 \\ 0.000678 \\ 0.000678 \\ 0.000387 \\ 0.000387 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.013347 \\ 0.01507 \\ 0.00874 \\ 0.008776 \\ 0 \\ 0.007081 \\ 1.99353 \\ 0.013348 \\ 0.013252 \\ 0.017587 \\ 0.021435 \\ 0.017134 \\ 0.017381 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 0.968218 \\ 0.965454e^{i0.994\pi} \\ 0.965454e^{-i0.994\pi} \\ 0.964372e^{i0.982\pi} \\ 0.964372e^{-i0.982\pi} \\ 0.961231e^{i0.989\pi} \\ 0.961231e^{-i0.989\pi} \\ 0.961069e^{i0.004\pi} \\ 0.961069e^{-i0.004\pi} \\ 0.960184e^{i0.030\pi} \\ 0.960184e^{-i0.030\pi} \\ 0.958621e^{i0.976\pi} \\ 0.958621e^{-i0.976\pi} \\ 0.953279e^{i0.001\pi} \\ 0.953279e^{-i0.001\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04074 \\ 0.083948e^{i0.267\pi} \\ 0.083948e^{i0.267\pi} \\ 0.083218e^{i0.210\pi} \\ 0.083218e^{i0.210\pi} \\ 0.082867e^{i0.286\pi} \\ 0.082867e^{i0.286\pi} \\ 0.099533e^{i0.246\pi} \\ 0.099533e^{i0.246\pi} \\ 0.098065e^{i0.404\pi} \\ 0.098065e^{i0.404\pi} \\ 0.075274e^{i0.166\pi} \\ 0.075274e^{i0.166\pi} \\ 0.067802e^{i0.141\pi} \\ 0.067802e^{i0.141\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.972876 \\ 0.974809e^{i0.990\pi} \\ 0.974809e^{-i0.990\pi} \\ 0.964248e^{i0.986\pi} \\ 0.964248e^{-i0.986\pi} \\ 0.956997e^{i0.990\pi} \\ 0.956997e^{-i0.990\pi} \\ 0.953006e^{i0.005\pi} \\ 0.953006e^{-i0.005\pi} \\ 0.95882e^{i0.024\pi} \\ 0.95882e^{-i0.024\pi} \\ 0.954763e^{i0.985\pi} \\ 0.954763e^{-i0.985\pi} \\ 0.95486 \\ 0.963923 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004658 \\ 0.016268 \\ 0.016268 \\ 0.012038 \\ 0.012038 \\ 0.006274 \\ 0.006274 \\ 0.008435 \\ 0.008435 \\ 0.016693 \\ 0.016693 \\ 0.026175 \\ 0.026175 \\ 0.002316 \\ 0.010778 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04074 \\ 0.083948 \\ 0.083948 \\ 0.083218 \\ 0.083218 \\ 0.082867 \\ 0.082867 \\ 0.099533 \\ 0.099533 \\ 0.098065 \\ 0.098065 \\ 0.075274 \\ 0.075274 \\ 0.067802 \\ 0.067802 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.058044 \\ 0.058955 \\ 0.058955 \\ 0.070179 \\ 0.070179 \\ 0.080116 \\ 0.080116 \\ 0.084098 \\ 0.084098 \\ 0.079494 \\ 0.079494 \\ 0.085079 \\ 0.085079 \\ 0.089753 \\ 0.081114 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039634 \\ 0.052853 \\ 0.056387 \\ 0.060506 \\ 0.066031 \\ 0.047809 \\ 0.050819 \\ 0.068937 \\ 0.066796 \\ 0.030023 \\ 0.025755 \\ 0.059258 \\ 0.065241 \\ 0.058468 \\ 0.059023 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.032298 \\ -0.035156 \\ -0.035156 \\ -0.036278 \\ -0.036278 \\ -0.039541 \\ -0.039541 \\ -0.039709 \\ -0.039709 \\ -0.04063 \\ -0.04063 \\ -0.04226 \\ -0.04226 \\ -0.047847 \\ -0.047847 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041216 \\ -0.056104 \\ -0.058809 \\ -0.065397 \\ -0.072218 \\ -0.049909 \\ -0.055206 \\ 0.07457 \\ 0.072924 \\ 0.042711 \\ 0.02567 \\ -0.066062 \\ -0.072803 \\ 0.062714 \\ 0.062618 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.994071 \\ -0.994071 \\ 0.982138 \\ -0.982138 \\ 0.988753 \\ -0.988753 \\ 0.004196 \\ -0.004196 \\ 0.029828 \\ -0.029828 \\ 0.976101 \\ -0.976101 \\ 0.000565 \\ -0.000565 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.022169 \\ 1.978503 \\ -0.01929 \\ -0.016804 \\ -0.023224 \\ 1.97793 \\ 0.021098 \\ 0.021713 \\ 0.028782 \\ 0.03105 \\ -0.015003 \\ -0.011605 \\ 0.009098 \\ 0.009167 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.004799 \\ 0.009642 \\ 0.009642 \\ 0.000128 \\ 0.000128 \\ 0.004414 \\ 0.004414 \\ 0.008425 \\ 0.008425 \\ 0.001422 \\ 0.001422 \\ 0.004032 \\ 0.004032 \\ 0.001657 \\ 0.011103 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041216 \\ 0.056104 \\ 0.058809 \\ 0.065397 \\ 0.072218 \\ 0.049909 \\ 0.055206 \\ 0.07457 \\ 0.072924 \\ 0.042711 \\ 0.02567 \\ 0.066062 \\ 0.072803 \\ 0.062714 \\ 0.062618 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.004367 \\ 0.004367 \\ 0.003974 \\ 0.003974 \\ 0.001537 \\ 0.001537 \\ 0.000824 \\ 0.000824 \\ 0.005519 \\ 0.005519 \\ 0.008614 \\ 0.008614 \\ 0.000565 \\ 0.000565 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.022169 \\ 1.978503 \\ 0.01929 \\ 0.016804 \\ 0.023224 \\ 1.97793 \\ 0.021098 \\ 0.021713 \\ 0.028782 \\ 0.03105 \\ 0.015003 \\ 0.011605 \\ 0.009098 \\ 0.009167 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | $ \begin{pmatrix} 1 \\ 0.973449e^{i0.676\pi} \\ 0.973449e^{-i0.676\pi} \\ 0.972712 \\ 0.968836e^{i0.007\pi} \\ 0.968836e^{-i0.007\pi} \\ 0.965701e^{i0.670\pi} \\ 0.965701e^{-i0.670\pi} \\ 0.965045 \\ 0.962978e^{i0.675\pi} \\ 0.962978e^{-i0.675\pi} \\ 0.962348e^{i0.669\pi} \\ 0.962348e^{-i0.669\pi} \\ 0.957771 \\ 0.954802e^{i0.655\pi} \\ 0.954802e^{-i0.655\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.053575e^{i0.223\pi} \\ 0.053575e^{i0.223\pi} \\ 0.05266 \\ 0.035119e^{i0.333\pi} \\ 0.035119e^{i0.333\pi} \\ 0.076826e^{i0.309\pi} \\ 0.076826e^{i0.309\pi} \\ 0.034133 \\ 0.096933e^{i0.245\pi} \\ 0.096933e^{i0.245\pi} \\ 0.130691e^{i0.219\pi} \\ 0.130691e^{i0.219\pi} \\ 0.100893 \\ 0.105384e^{i0.208\pi} \\ 0.105384e^{i0.208\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.975831e^{i0.672\pi} \\ 0.975831e^{-i0.672\pi} \\ 0.974564 \\ 0.96733e^{i0.002\pi} \\ 0.96733e^{-i0.002\pi} \\ 0.966254e^{i0.671\pi} \\ 0.966254e^{-i0.671\pi} \\ 0.965865 \\ 0.95876e^{i0.672\pi} \\ 0.95876e^{-i0.672\pi} \\ 0.963091e^{i0.669\pi} \\ 0.963091e^{-i0.669\pi} \\ 0.957152 \\ 0.955857e^{i0.658\pi} \\ 0.955857e^{-i0.658\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.013768 \\ 0.013768 \\ 0.001852 \\ 0.013821 \\ 0.013821 \\ 0.002812 \\ 0.002812 \\ 0.000821 \\ 0.011291 \\ 0.011291 \\ 0.000944 \\ 0.000944 \\ 0.000619 \\ 0.01033 \\ 0.01033 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.053575 \\ 0.053575 \\ 0.05266 \\ 0.035119 \\ 0.035119 \\ 0.076826 \\ 0.076826 \\ 0.034133 \\ 0.096933 \\ 0.096933 \\ 0.130691 \\ 0.130691 \\ 0.100893 \\ 0.105384 \\ 0.105384 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.05017 \\ 0.05017 \\ 0.05203 \\ 0.06291 \\ 0.06291 \\ 0.066892 \\ 0.066892 \\ 0.067897 \\ 0.07679 \\ 0.07679 \\ 0.073172 \\ 0.073172 \\ 0.083267 \\ 0.087398 \\ 0.087398 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013772 \\ 0.054803 \\ 0.05132 \\ 0.017118 \\ 0.016853 \\ 0.014597 \\ 0.057565 \\ 0.032968 \\ 0.023011 \\ 0.091504 \\ 0.034491 \\ 0.133131 \\ 0.09657 \\ 0.032182 \\ 0.108547 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.02691 \\ -0.02691 \\ -0.027668 \\ -0.031659 \\ -0.031659 \\ -0.034901 \\ -0.034901 \\ -0.035581 \\ -0.037725 \\ -0.037725 \\ -0.038379 \\ -0.038379 \\ -0.043146 \\ -0.046251 \\ -0.046251 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009527 \\ -0.053551 \\ 0.052723 \\ 0.019098 \\ 0.017768 \\ 0.035429 \\ -0.082687 \\ 0.034758 \\ 0.026337 \\ -0.102214 \\ 0.029509 \\ -0.134951 \\ 0.100154 \\ 0.023734 \\ -0.104292 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.676059 \\ -0.676059 \\ 0 \\ 0.006996 \\ -0.006996 \\ 0.670042 \\ -0.670042 \\ 0 \\ 0.675049 \\ -0.675049 \\ 0.669116 \\ -0.669116 \\ 0 \\ 0.654831 \\ -0.654831 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.017172 \\ 0.005758 \\ 0 \\ 0.009678 \\ 0.00994 \\ -0.02218 \\ 0.001843 \\ 0 \\ -0.030502 \\ 0.00881 \\ -0.041575 \\ 0.017049 \\ 0 \\ -0.033902 \\ 0.01634 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002444 \\ 0.002444 \\ 0.001903 \\ 0.001556 \\ 0.001556 \\ 0.000572 \\ 0.000572 \\ 0.00085 \\ 0.004389 \\ 0.004389 \\ 0.000772 \\ 0.000772 \\ 0.000647 \\ 0.001104 \\ 0.001104 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009527 \\ 0.053551 \\ 0.052723 \\ 0.019098 \\ 0.017768 \\ 0.035429 \\ 0.082687 \\ 0.034758 \\ 0.026337 \\ 0.102214 \\ 0.029509 \\ 0.134951 \\ 0.100154 \\ 0.023734 \\ 0.104292 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004429 \\ 0.004429 \\ 0 \\ 0.004517 \\ 0.004517 \\ 0.000909 \\ 0.000909 \\ 0 \\ 0.00347 \\ 0.00347 \\ 0.000192 \\ 0.000192 \\ 0 \\ 0.003424 \\ 0.003424 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.017172 \\ 0.005758 \\ 0 \\ 0.009678 \\ 0.00994 \\ 0.02218 \\ 0.001843 \\ 0 \\ 0.030502 \\ 0.00881 \\ 0.041575 \\ 0.017049 \\ 0 \\ 0.033902 \\ 0.01634 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 0.941908 \\ 0.934951e^{i0.997\pi} \\ 0.934951e^{-i0.997\pi} \\ 0.934088 \\ 0.933979e^{i0.983\pi} \\ 0.933979e^{-i0.983\pi} \\ 0.928567e^{i0.023\pi} \\ 0.928567e^{-i0.023\pi} \\ 0.92721e^{i0.984\pi} \\ 0.92721e^{-i0.984\pi} \\ 0.91776e^{i0.013\pi} \\ 0.91776e^{-i0.013\pi} \\ 0.917178e^{i0.990\pi} \\ 0.917178e^{-i0.990\pi} \\ 0.911384 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041915 \\ 0.089722e^{i0.270\pi} \\ 0.089722e^{i0.270\pi} \\ 0.118509 \\ 0.129413e^{i0.240\pi} \\ 0.129413e^{i0.240\pi} \\ 0.076064e^{i0.171\pi} \\ 0.076064e^{i0.171\pi} \\ 0.15804e^{i0.253\pi} \\ 0.15804e^{i0.253\pi} \\ 0.088432e^{i0.171\pi} \\ 0.088432e^{i0.171\pi} \\ 0.07926e^{i0.192\pi} \\ 0.07926e^{i0.192\pi} \\ 0.061055 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.939091 \\ -0.936983 \\ -0.928601 \\ 0.924899e^{i0.001\pi} \\ 0.940472e^{i0.995\pi} \\ 0.940472e^{-i0.995\pi} \\ 0.932991e^{i0.005\pi} \\ 0.932991e^{-i0.005\pi} \\ 0.928191e^{i0.996\pi} \\ 0.928191e^{-i0.996\pi} \\ 0.912877e^{i0.005\pi} \\ 0.912877e^{-i0.005\pi} \\ 0.911691e^{i0.994\pi} \\ 0.911691e^{-i0.994\pi} \\ 0.924899e^{-i0.001\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002817 \\ 0.010106 \\ 0.011723 \\ 0.00958 \\ 0.034884 \\ 0.034884 \\ 0.053449 \\ 0.053449 \\ 0.03405 \\ 0.03405 \\ 0.02385 \\ 0.02385 \\ 0.01201 \\ 0.01201 \\ 0.013778 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041915 \\ 0.089722 \\ 0.089722 \\ 0.118509 \\ 0.129413 \\ 0.129413 \\ 0.076064 \\ 0.076064 \\ 0.15804 \\ 0.15804 \\ 0.088432 \\ 0.088432 \\ 0.07926 \\ 0.07926 \\ 0.061055 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.115463 \\ 0.124016 \\ 0.131852 \\ 0.136067 \\ 0.122206 \\ 0.122206 \\ 0.135074 \\ 0.135074 \\ 0.139951 \\ 0.139951 \\ 0.162471 \\ 0.162471 \\ 0.163874 \\ 0.163874 \\ 0.157065 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039362 \\ 0.055643 \\ 0.055145 \\ 0.109928 \\ 0.087118 \\ 0.09018 \\ 0.061918 \\ 0.05998 \\ 0.10146 \\ 0.104187 \\ 0.070469 \\ 0.068247 \\ 0.058367 \\ 0.06054 \\ 0.056305 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.059848 \\ -0.067262 \\ -0.067262 \\ -0.068185 \\ -0.068301 \\ -0.068301 \\ -0.074112 \\ -0.074112 \\ -0.075575 \\ -0.075575 \\ -0.08582 \\ -0.08582 \\ -0.086453 \\ -0.086453 \\ -0.09279 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.043538 \\ -0.061816 \\ -0.063541 \\ 0.119445 \\ -0.094473 \\ -0.106969 \\ 0.071264 \\ 0.06592 \\ -0.11 \\ -0.125359 \\ 0.08226 \\ 0.078777 \\ -0.070639 \\ -0.074038 \\ 0.064844 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.996633 \\ -0.996633 \\ 0 \\ 0.982861 \\ -0.982861 \\ 0.023279 \\ -0.023279 \\ 0.984101 \\ -0.984101 \\ 0.013216 \\ -0.013216 \\ 0.990465 \\ -0.990465 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.024609 \\ 1.975806 \\ 0 \\ -0.035133 \\ 1.968294 \\ 0.010879 \\ 0.014004 \\ -0.045411 \\ 1.958228 \\ 0.013434 \\ 0.015505 \\ -0.017502 \\ 1.9839 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002995 \\ 0.002172 \\ 0.006814 \\ 0.009885 \\ 0.006927 \\ 0.006927 \\ 0.004752 \\ 0.004752 \\ 0.001058 \\ 0.001058 \\ 0.005335 \\ 0.005335 \\ 0.006001 \\ 0.006001 \\ 0.01472 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.043538 \\ 0.061816 \\ 0.063541 \\ 0.119445 \\ 0.094473 \\ 0.106969 \\ 0.071264 \\ 0.06592 \\ 0.11 \\ 0.125359 \\ 0.08226 \\ 0.078777 \\ 0.070639 \\ 0.074038 \\ 0.064844 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.003367 \\ 1.996633 \\ 0.000929 \\ 0.011642 \\ 0.011642 \\ 0.018219 \\ 0.018219 \\ 0.011679 \\ 0.011679 \\ 0.008119 \\ 0.008119 \\ 0.003719 \\ 0.003719 \\ 0.000929 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.024609 \\ 1.975806 \\ 0 \\ 0.035133 \\ 1.968294 \\ 0.010879 \\ 0.014004 \\ 0.045411 \\ 1.958228 \\ 0.013434 \\ 0.015505 \\ 0.017502 \\ 1.9839 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.969632 \\ 0.966787e^{i0.995\pi} \\ 0.966787e^{-i0.995\pi} \\ 0.946012e^{i0.006\pi} \\ 0.946012e^{-i0.006\pi} \\ 0.944607e^{i0.988\pi} \\ 0.944607e^{-i0.988\pi} \\ 0.944118 \\ 0.942092e^{i0.992\pi} \\ 0.942092e^{-i0.992\pi} \\ 0.93863 \\ 0.936176e^{i0.996\pi} \\ 0.936176e^{-i0.996\pi} \\ 0.930313e^{i0.014\pi} \\ 0.930313e^{-i0.014\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032186 \\ 0.031875e^{i0.267\pi} \\ 0.031875e^{i0.267\pi} \\ 0.112308e^{i0.124\pi} \\ 0.112308e^{i0.124\pi} \\ 0.075543e^{i0.193\pi} \\ 0.075543e^{i0.193\pi} \\ 0.088742 \\ 0.116515e^{i0.213\pi} \\ 0.116515e^{i0.213\pi} \\ 0.133314 \\ 0.157104e^{i0.263\pi} \\ 0.157104e^{i0.263\pi} \\ 0.103492e^{i0.219\pi} \\ 0.103492e^{i0.219\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.967227 \\ -0.965275 \\ -0.969322 \\ 0.940756e^{i0.011\pi} \\ 0.940756e^{-i0.011\pi} \\ 0.948274e^{i0.988\pi} \\ 0.948274e^{-i0.988\pi} \\ 0.946884 \\ 0.938569e^{i0.989\pi} \\ 0.938569e^{-i0.989\pi} \\ 0.93643 \\ 0.936998e^{i1.000\pi} \\ 0.936998e^{-i1.000\pi} \\ 0.93497e^{i0.011\pi} \\ 0.93497e^{-i0.011\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002406 \\ 0.013845 \\ 0.014022 \\ 0.014346 \\ 0.014346 \\ 0.003929 \\ 0.003929 \\ 0.002766 \\ 0.007982 \\ 0.007982 \\ 0.0022 \\ 0.009569 \\ 0.009569 \\ 0.00998 \\ 0.00998 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032186 \\ 0.031875 \\ 0.031875 \\ 0.112308 \\ 0.112308 \\ 0.075543 \\ 0.075543 \\ 0.088742 \\ 0.116515 \\ 0.116515 \\ 0.133314 \\ 0.157104 \\ 0.157104 \\ 0.103492 \\ 0.103492 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.062146 \\ 0.06688 \\ 0.062967 \\ 0.110122 \\ 0.110122 \\ 0.104255 \\ 0.104255 \\ 0.10603 \\ 0.115807 \\ 0.115807 \\ 0.121039 \\ 0.12285 \\ 0.12285 \\ 0.130225 \\ 0.130225 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.031132 \\ 0.020568 \\ 0.020654 \\ 0.101097 \\ 0.094342 \\ 0.056676 \\ 0.060969 \\ 0.084029 \\ 0.082842 \\ 0.088651 \\ 0.124839 \\ 0.099742 \\ 0.100006 \\ 0.077178 \\ 0.072188 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.030838 \\ -0.033777 \\ -0.033777 \\ -0.0555 \\ -0.0555 \\ -0.056986 \\ -0.056986 \\ -0.057504 \\ -0.059652 \\ -0.059652 \\ -0.063334 \\ -0.065951 \\ -0.065951 \\ -0.072234 \\ -0.072234 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032655 \\ -0.021605 \\ -0.022335 \\ 0.105785 \\ 0.104298 \\ -0.064755 \\ -0.068709 \\ 0.089836 \\ -0.095987 \\ -0.100887 \\ 0.132808 \\ -0.109514 \\ -0.113057 \\ 0.087015 \\ 0.0819 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.995465 \\ -0.995465 \\ 0.006493 \\ -0.006493 \\ 0.987914 \\ -0.987914 \\ 0 \\ 0.991646 \\ -0.991646 \\ 0 \\ 0.996339 \\ -0.996339 \\ 0.013642 \\ -0.013642 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.008078 \\ 1.992121 \\ 0.012239 \\ 0.013543 \\ -0.016322 \\ 1.985316 \\ 0 \\ -0.027789 \\ 1.973874 \\ 0 \\ -0.044389 \\ 1.956395 \\ 0.019541 \\ 0.021805 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002484 \\ 0.001565 \\ 0.002619 \\ 0.005571 \\ 0.005571 \\ 0.003874 \\ 0.003874 \\ 0.002925 \\ 0.003747 \\ 0.003747 \\ 0.002347 \\ 0.000877 \\ 0.000877 \\ 0.004993 \\ 0.004993 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032655 \\ 0.021605 \\ 0.022335 \\ 0.105785 \\ 0.104298 \\ 0.064755 \\ 0.068709 \\ 0.089836 \\ 0.095987 \\ 0.100887 \\ 0.132808 \\ 0.109514 \\ 0.113057 \\ 0.087015 \\ 0.0819 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.004535 \\ 1.995465 \\ 0.004504 \\ 0.004504 \\ 0.000474 \\ 0.000474 \\ 0 \\ 0.002424 \\ 0.002424 \\ 0 \\ 0.00324 \\ 0.00324 \\ 0.003013 \\ 0.003013 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.008078 \\ 1.992121 \\ 0.012239 \\ 0.013543 \\ 0.016322 \\ 1.985316 \\ 0 \\ 0.027789 \\ 1.973874 \\ 0 \\ 0.044389 \\ 1.956395 \\ 0.019541 \\ 0.021805 \end{pmatrix} $ π |
| Gate or Germ | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222e^{i0.422\pi} \\ 0.02222e^{i0.422\pi} \\ 0.046623e^{i0.386\pi} \\ 0.046623e^{i0.386\pi} \\ 0.042233e^{i0.370\pi} \\ 0.042233e^{i0.370\pi} \\ 0.099689 \\ 0.070182e^{i0.296\pi} \\ 0.070182e^{i0.296\pi} \\ 0.05523e^{i0.308\pi} \\ 0.05523e^{i0.308\pi} \\ 0.06728e^{i0.202\pi} \\ 0.06728e^{i0.202\pi} \\ 0.046658e^{i0.368\pi} \\ 0.046658e^{i0.368\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222 \\ 0.02222 \\ 0.046623 \\ 0.046623 \\ 0.042233 \\ 0.042233 \\ 0.099689 \\ 0.070182 \\ 0.070182 \\ 0.05523 \\ 0.05523 \\ 0.06728 \\ 0.06728 \\ 0.046658 \\ 0.046658 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.00257 \\ 0.00257 \\ 0.012193 \\ 0.012193 \\ 0.012224 \\ 0.012224 \\ 0.014733 \\ 0.017438 \\ 0.017438 \\ 0.023711 \\ 0.023711 \\ 0.027921 \\ 0.027921 \\ 0.028122 \\ 0.028122 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005399 \\ 0.005398 \\ 0.016393 \\ 0.016117 \\ 0.016967 \\ 0.01635 \\ 0.098952 \\ 0.042029 \\ 0.041071 \\ 0.031033 \\ 0.030972 \\ 0.053862 \\ 0.053096 \\ 0.01884 \\ 0.01812 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001287 \\ -0.001287 \\ -0.006134 \\ -0.006134 \\ -0.00615 \\ -0.00615 \\ -0.007422 \\ -0.008796 \\ -0.008796 \\ -0.011998 \\ -0.011998 \\ -0.014159 \\ -0.014159 \\ -0.014262 \\ -0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000039 \\ -0.000039 \\ 0.002706 \\ -0.002706 \\ 0.005895 \\ -0.005895 \\ 0 \\ 0.003668 \\ -0.003668 \\ 0.000315 \\ -0.000315 \\ 0.002279 \\ -0.002279 \\ 0.006197 \\ -0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203e^{i0.125\pi} \\ 0.009203e^{i0.125\pi} \\ 0.01311e^{i0.170\pi} \\ 0.01311e^{i0.170\pi} \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025e^{i0.364\pi} \\ 0.031025e^{i0.364\pi} \\ 0.044919e^{i0.256\pi} \\ 0.044919e^{i0.256\pi} \\ 0.02034e^{i0.335\pi} \\ 0.02034e^{i0.335\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203 \\ 0.009203 \\ 0.01311 \\ 0.01311 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025 \\ 0.031025 \\ 0.044919 \\ 0.044919 \\ 0.02034 \\ 0.02034 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002599 \\ 0.00735 \\ 0.00735 \\ 0.007577 \\ 0.007577 \\ 0.009852 \\ 0.014906 \\ 0.02303 \\ 0.027968 \\ 0.029773 \\ 0.029773 \\ 0.030519 \\ 0.030519 \\ 0.035655 \\ 0.035655 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003614 \\ 0.008461 \\ 0.008471 \\ 0.011253 \\ 0.011234 \\ 0.005281 \\ 0.076958 \\ 0.093222 \\ 0.042548 \\ 0.012626 \\ 0.012646 \\ 0.03072 \\ 0.030657 \\ 0.009896 \\ 0.009875 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001301 \\ -0.003689 \\ -0.003689 \\ -0.003803 \\ -0.003803 \\ -0.00495 \\ -0.007509 \\ -0.011649 \\ -0.014183 \\ -0.015112 \\ -0.015112 \\ -0.015497 \\ -0.015497 \\ -0.018153 \\ -0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ -0.003522 \\ 0.006745 \\ -0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ -0.029019 \\ 0.032824 \\ -0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.500184 \\ -0.500184 \\ 0.499738 \\ -0.499738 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.500251 \\ -0.500251 \\ 0.499672 \\ -0.499672 \\ 0.000331 \\ -0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002706 \\ 0.002724 \\ -0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ -0.004037 \\ 0.00426 \\ -0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ 0.003522 \\ 0.006745 \\ 0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ 0.029019 \\ 0.032824 \\ 0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002706 \\ 0.002724 \\ 0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.004037 \\ 0.00426 \\ 0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449e^{i0.334\pi} \\ 0.008449e^{i0.334\pi} \\ 0.012314e^{i0.259\pi} \\ 0.012314e^{i0.259\pi} \\ 0.034277e^{i0.312\pi} \\ 0.034277e^{i0.312\pi} \\ 0.024184e^{i0.192\pi} \\ 0.024184e^{i0.192\pi} \\ 0.034863e^{i0.265\pi} \\ 0.034863e^{i0.265\pi} \\ 0.009148 \\ 0.055108e^{i0.418\pi} \\ 0.055108e^{i0.418\pi} \\ 0.013582 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449 \\ 0.008449 \\ 0.012314 \\ 0.012314 \\ 0.034277 \\ 0.034277 \\ 0.024184 \\ 0.024184 \\ 0.034863 \\ 0.034863 \\ 0.009148 \\ 0.055108 \\ 0.055108 \\ 0.013582 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.004267 \\ 0.012432 \\ 0.012432 \\ 0.012565 \\ 0.012565 \\ 0.02002 \\ 0.02002 \\ 0.020031 \\ 0.020031 \\ 0.020069 \\ 0.020069 \\ 0.02045 \\ 0.020589 \\ 0.020589 \\ 0.023137 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008761 \\ 0.004115 \\ 0.00425 \\ 0.008097 \\ 0.008688 \\ 0.017814 \\ 0.019906 \\ 0.019811 \\ 0.019649 \\ 0.024086 \\ 0.022299 \\ 0.009054 \\ 0.014253 \\ 0.013668 \\ 0.013424 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002138 \\ -0.006255 \\ -0.006255 \\ -0.006322 \\ -0.006322 \\ -0.010112 \\ -0.010112 \\ -0.010117 \\ -0.010117 \\ -0.010136 \\ -0.010136 \\ -0.010331 \\ -0.010402 \\ -0.010402 \\ -0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ -0.007458 \\ 0.008709 \\ -0.009316 \\ 0.027483 \\ -0.030075 \\ 0.01402 \\ -0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.505124 \\ -0.505124 \\ 0.511209 \\ -0.511209 \\ 0.517641 \\ -0.517641 \\ 0.498692 \\ -0.498692 \\ 0.012255 \\ -0.012255 \\ 0 \\ 0.006668 \\ -0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.001376 \\ 0.00132 \\ -0.002782 \\ 0.002629 \\ -0.006454 \\ 0.005791 \\ -0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ 0.007458 \\ 0.008709 \\ 0.009316 \\ 0.027483 \\ 0.030075 \\ 0.01402 \\ 0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.001376 \\ 0.00132 \\ 0.002782 \\ 0.002629 \\ 0.006454 \\ 0.005791 \\ 0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056e^{i0.308\pi} \\ 0.016056e^{i0.308\pi} \\ 0.030592e^{i0.157\pi} \\ 0.030592e^{i0.157\pi} \\ 0.034405e^{i0.146\pi} \\ 0.034405e^{i0.146\pi} \\ 0.062388e^{i0.187\pi} \\ 0.062388e^{i0.187\pi} \\ 0.040223e^{i0.084\pi} \\ 0.040223e^{i0.084\pi} \\ 0.014925 \\ 0.121571e^{i0.056\pi} \\ 0.121571e^{i0.056\pi} \\ 0.063247 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056 \\ 0.016056 \\ 0.030592 \\ 0.030592 \\ 0.034405 \\ 0.034405 \\ 0.062388 \\ 0.062388 \\ 0.040223 \\ 0.040223 \\ 0.014925 \\ 0.121571 \\ 0.121571 \\ 0.063247 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.005921 \\ 0.01089 \\ 0.01089 \\ 0.019329 \\ 0.019329 \\ 0.019957 \\ 0.019957 \\ 0.021936 \\ 0.021936 \\ 0.022035 \\ 0.022035 \\ 0.028506 \\ 0.031215 \\ 0.031215 \\ 0.032944 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010678 \\ 0.009033 \\ 0.00912 \\ 0.027419 \\ 0.025895 \\ 0.031643 \\ 0.02935 \\ 0.049415 \\ 0.053303 \\ 0.039475 \\ 0.037301 \\ 0.01471 \\ 0.117241 \\ 0.118357 \\ 0.062197 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.002969 \\ -0.005475 \\ -0.005475 \\ -0.009759 \\ -0.009759 \\ -0.01008 \\ -0.01008 \\ -0.01109 \\ -0.01109 \\ -0.011141 \\ -0.011141 \\ -0.01446 \\ -0.015856 \\ -0.015856 \\ -0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ -0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ -0.036151 \\ 0.012379 \\ -0.008731 \\ 0.015028 \\ 0.02794 \\ -0.01485 \\ 0.062332 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.501519 \\ -0.501519 \\ 0.009095 \\ -0.009095 \\ 0.011962 \\ -0.011962 \\ 0.512043 \\ -0.512043 \\ 0.490987 \\ -0.490987 \\ 0 \\ 0.501508 \\ -0.501508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ -0.016574 \\ 0.016902 \\ -0.01225 \\ 0.012704 \\ 0 \\ -0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ 0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ 0.036151 \\ 0.012379 \\ 0.008731 \\ 0.015028 \\ 0.02794 \\ 0.01485 \\ 0.062332 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ 0.016574 \\ 0.016902 \\ 0.01225 \\ 0.012704 \\ 0 \\ 0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424e^{i0.187\pi} \\ 0.009424e^{i0.187\pi} \\ 0.021644e^{i0.074\pi} \\ 0.021644e^{i0.074\pi} \\ 0.02175 \\ 0.034408 \\ 0.059387e^{i0.446\pi} \\ 0.059387e^{i0.446\pi} \\ 0.074565e^{i0.208\pi} \\ 0.074565e^{i0.208\pi} \\ 0.041644e^{i0.259\pi} \\ 0.041644e^{i0.259\pi} \\ 0.042314e^{i0.321\pi} \\ 0.042314e^{i0.321\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424 \\ 0.009424 \\ 0.021644 \\ 0.021644 \\ 0.02175 \\ 0.034408 \\ 0.059387 \\ 0.059387 \\ 0.074565 \\ 0.074565 \\ 0.041644 \\ 0.041644 \\ 0.042314 \\ 0.042314 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001995 \\ 0.007797 \\ 0.007797 \\ 0.007957 \\ 0.007957 \\ 0.014204 \\ 0.014544 \\ 0.033034 \\ 0.033034 \\ 0.033129 \\ 0.033129 \\ 0.033587 \\ 0.033587 \\ 0.033608 \\ 0.033608 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003304 \\ 0.007745 \\ 0.007887 \\ 0.0205 \\ 0.02144 \\ 0.021595 \\ 0.034156 \\ 0.00924 \\ 0.010339 \\ 0.060901 \\ 0.055537 \\ 0.029116 \\ 0.027171 \\ 0.022717 \\ 0.02163 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.000998 \\ -0.003914 \\ -0.003914 \\ -0.003994 \\ -0.003994 \\ -0.007153 \\ -0.007326 \\ -0.016796 \\ -0.016796 \\ -0.016845 \\ -0.016845 \\ -0.017082 \\ -0.017082 \\ -0.017093 \\ -0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ -0.005293 \\ 0.004755 \\ -0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ -0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ -0.036192 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.502902 \\ -0.502902 \\ 0.507134 \\ -0.507134 \\ 0 \\ 0 \\ 0.517844 \\ -0.517844 \\ 0.014652 \\ -0.014652 \\ 0.010997 \\ -0.010997 \\ 0.492193 \\ -0.492193 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00251 \\ 0.002506 \\ -0.006733 \\ 0.006729 \\ 0 \\ 0 \\ -0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ -0.006768 \\ 0.007868 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ 0.005293 \\ 0.004755 \\ 0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ 0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ 0.036192 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00251 \\ 0.002506 \\ 0.006733 \\ 0.006729 \\ 0 \\ 0 \\ 0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ 0.006768 \\ 0.007868 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446e^{i0.154\pi} \\ 0.05446e^{i0.154\pi} \\ 0.029927e^{i0.115\pi} \\ 0.029927e^{i0.115\pi} \\ 0.026108e^{i0.316\pi} \\ 0.026108e^{i0.316\pi} \\ 0.060803e^{i0.249\pi} \\ 0.060803e^{i0.249\pi} \\ 0.045035e^{i0.412\pi} \\ 0.045035e^{i0.412\pi} \\ 0.096531e^{i0.422\pi} \\ 0.096531e^{i0.422\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446 \\ 0.05446 \\ 0.029927 \\ 0.029927 \\ 0.026108 \\ 0.026108 \\ 0.060803 \\ 0.060803 \\ 0.045035 \\ 0.045035 \\ 0.096531 \\ 0.096531 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.002885 \\ 0.009475 \\ 0.012728 \\ 0.034389 \\ 0.034389 \\ 0.034579 \\ 0.034579 \\ 0.035609 \\ 0.035609 \\ 0.036388 \\ 0.036388 \\ 0.062746 \\ 0.062746 \\ 0.063697 \\ 0.063697 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005053 \\ 0.024726 \\ 0.01211 \\ 0.049843 \\ 0.044773 \\ 0.028299 \\ 0.02666 \\ 0.013147 \\ 0.014769 \\ 0.038765 \\ 0.045682 \\ 0.012234 \\ 0.011687 \\ 0.022021 \\ 0.023302 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.001445 \\ -0.00476 \\ -0.006405 \\ -0.017497 \\ -0.017497 \\ -0.017595 \\ -0.017595 \\ -0.018129 \\ -0.018129 \\ -0.018533 \\ -0.018533 \\ -0.0324 \\ -0.0324 \\ -0.032908 \\ -0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ -0.012995 \\ -0.015655 \\ -0.039888 \\ -0.047663 \\ 0.014649 \\ 0.012659 \\ -0.016771 \\ -0.022458 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ -0.017039 \\ 0.009491 \\ -0.009491 \\ 0.98153 \\ -0.98153 \\ 0.973987 \\ -0.973987 \\ 0.007277 \\ -0.007277 \\ 0.991007 \\ -0.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ -0.007446 \\ -0.006922 \\ -0.0156 \\ -0.013324 \\ 0.013941 \\ 0.014152 \\ -0.031587 \\ 1.96868 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ 0.012995 \\ 0.015655 \\ 0.039888 \\ 0.047663 \\ 0.014649 \\ 0.012659 \\ 0.016771 \\ 0.022458 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ 0.007446 \\ 0.006922 \\ 0.0156 \\ 0.013324 \\ 0.013941 \\ 0.014152 \\ 0.031587 \\ 1.96868 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | $ \begin{pmatrix} 1 \\ 0.995962 \\ 0.988919 \\ 0.987067e^{i0.680\pi} \\ 0.987067e^{-i0.680\pi} \\ 0.985827e^{i0.678\pi} \\ 0.985827e^{-i0.678\pi} \\ 0.985772 \\ 0.979111e^{i0.022\pi} \\ 0.979111e^{-i0.022\pi} \\ 0.97333e^{i0.022\pi} \\ 0.97333e^{-i0.022\pi} \\ 0.971183e^{i0.701\pi} \\ 0.971183e^{-i0.701\pi} \\ 0.97097e^{i0.657\pi} \\ 0.97097e^{-i0.657\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007162 \\ 0.020505 \\ 0.042873e^{i0.316\pi} \\ 0.042873e^{i0.316\pi} \\ 0.040824e^{i0.327\pi} \\ 0.040824e^{i0.327\pi} \\ 0.029279 \\ 0.059198e^{i0.281\pi} \\ 0.059198e^{i0.281\pi} \\ 0.114171e^{i0.300\pi} \\ 0.114171e^{i0.300\pi} \\ 0.072115e^{i0.260\pi} \\ 0.072115e^{i0.260\pi} \\ 0.113361e^{i0.347\pi} \\ 0.113361e^{i0.347\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.996706 \\ 0.987977 \\ 0.987009e^{i0.677\pi} \\ 0.987009e^{-i0.677\pi} \\ 0.987023e^{i0.671\pi} \\ 0.987023e^{-i0.671\pi} \\ 0.986092 \\ 0.975384e^{i0.019\pi} \\ 0.975384e^{-i0.019\pi} \\ 0.975905e^{i0.024\pi} \\ 0.975905e^{-i0.024\pi} \\ 0.971134e^{i0.696\pi} \\ 0.971134e^{-i0.696\pi} \\ 0.97098e^{i0.652\pi} \\ 0.97098e^{-i0.652\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000744 \\ 0.000942 \\ 0.009745 \\ 0.009745 \\ 0.021284 \\ 0.021284 \\ 0.00032 \\ 0.009003 \\ 0.009003 \\ 0.007286 \\ 0.007286 \\ 0.015968 \\ 0.015968 \\ 0.01458 \\ 0.01458 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007162 \\ 0.020505 \\ 0.042873 \\ 0.042873 \\ 0.040824 \\ 0.040824 \\ 0.029279 \\ 0.059198 \\ 0.059198 \\ 0.114171 \\ 0.114171 \\ 0.072115 \\ 0.072115 \\ 0.113361 \\ 0.113361 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.007318 \\ 0.022971 \\ 0.025804 \\ 0.025804 \\ 0.027191 \\ 0.027191 \\ 0.027938 \\ 0.045025 \\ 0.045025 \\ 0.050146 \\ 0.050146 \\ 0.056979 \\ 0.056979 \\ 0.057313 \\ 0.057313 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007139 \\ 0.020259 \\ 0.007423 \\ 0.031875 \\ 0.007216 \\ 0.028603 \\ 0.028871 \\ 0.038893 \\ 0.034409 \\ 0.070453 \\ 0.060374 \\ 0.011419 \\ 0.06694 \\ 0.021796 \\ 0.068763 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.004046 \\ -0.011143 \\ -0.013017 \\ -0.013017 \\ -0.014274 \\ -0.014274 \\ -0.01433 \\ -0.02111 \\ -0.02111 \\ -0.027032 \\ -0.027032 \\ -0.02924 \\ -0.02924 \\ -0.029459 \\ -0.029459 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007166 \\ 0.020523 \\ 0.018531 \\ -0.044403 \\ 0.019125 \\ -0.042287 \\ 0.029269 \\ 0.04164 \\ 0.035644 \\ 0.076276 \\ 0.064776 \\ 0.015971 \\ -0.076506 \\ 0.067531 \\ -0.124137 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.680314 \\ -0.680314 \\ 0.678196 \\ -0.678196 \\ 0 \\ 0.022115 \\ -0.022115 \\ 0.022248 \\ -0.022248 \\ 0.701451 \\ -0.701451 \\ 0.657073 \\ -0.657073 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.012364 \\ 0.000176 \\ -0.01155 \\ -0.000216 \\ 0 \\ 0.013401 \\ 0.015124 \\ 0.026502 \\ 0.029699 \\ -0.022895 \\ 0.00312 \\ -0.028796 \\ -0.000489 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000747 \\ 0.000953 \\ 0.000059 \\ 0.000059 \\ 0.001213 \\ 0.001213 \\ 0.000324 \\ 0.003814 \\ 0.003814 \\ 0.002642 \\ 0.002642 \\ 0.000051 \\ 0.000051 \\ 0.00001 \\ 0.00001 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007166 \\ 0.020523 \\ 0.018531 \\ 0.044403 \\ 0.019125 \\ 0.042287 \\ 0.029269 \\ 0.04164 \\ 0.035644 \\ 0.076276 \\ 0.064776 \\ 0.015971 \\ 0.076506 \\ 0.067531 \\ 0.124137 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.003143 \\ 0.003143 \\ 0.006857 \\ 0.006857 \\ 0 \\ 0.002669 \\ 0.002669 \\ 0.002226 \\ 0.002226 \\ 0.005234 \\ 0.005234 \\ 0.00478 \\ 0.00478 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.012364 \\ 0.000176 \\ 0.01155 \\ 0.000216 \\ 0 \\ 0.013401 \\ 0.015124 \\ 0.026502 \\ 0.029699 \\ 0.022895 \\ 0.00312 \\ 0.028796 \\ 0.000489 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.992912 \\ 0.983501e^{i0.667\pi} \\ 0.983501e^{-i0.667\pi} \\ 0.980519e^{i0.005\pi} \\ 0.980519e^{-i0.005\pi} \\ 0.980362e^{i0.014\pi} \\ 0.980362e^{-i0.014\pi} \\ 0.979734e^{i0.657\pi} \\ 0.979734e^{-i0.657\pi} \\ 0.979709e^{i0.678\pi} \\ 0.979709e^{-i0.678\pi} \\ 0.977076e^{i0.668\pi} \\ 0.977076e^{-i0.668\pi} \\ 0.968146 \\ 0.967558 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01368 \\ 0.177503e^{i0.145\pi} \\ 0.177503e^{i0.145\pi} \\ 0.04239e^{i0.284\pi} \\ 0.04239e^{i0.284\pi} \\ 0.041609e^{i0.243\pi} \\ 0.041609e^{i0.243\pi} \\ 0.051267e^{i0.066\pi} \\ 0.051267e^{i0.066\pi} \\ 0.093376e^{i0.266\pi} \\ 0.093376e^{i0.266\pi} \\ 0.250042e^{i0.138\pi} \\ 0.250042e^{i0.138\pi} \\ 0.074431 \\ 0.027949 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.993035 \\ 0.992584e^{i0.668\pi} \\ 0.992584e^{-i0.668\pi} \\ 0.980856e^{i0.009\pi} \\ 0.980856e^{-i0.009\pi} \\ 0.980368e^{i0.011\pi} \\ 0.980368e^{-i0.011\pi} \\ 0.979407e^{i0.658\pi} \\ 0.979407e^{-i0.658\pi} \\ 0.979479e^{i0.678\pi} \\ 0.979479e^{-i0.678\pi} \\ 0.968307e^{i0.668\pi} \\ 0.968307e^{-i0.668\pi} \\ 0.968061 \\ 0.967602 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000123 \\ 0.009097 \\ 0.009097 \\ 0.010386 \\ 0.010386 \\ 0.01036 \\ 0.01036 \\ 0.000893 \\ 0.000893 \\ 0.00043 \\ 0.00043 \\ 0.008769 \\ 0.008769 \\ 0.000084 \\ 0.000043 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01368 \\ 0.177503 \\ 0.177503 \\ 0.04239 \\ 0.04239 \\ 0.041609 \\ 0.041609 \\ 0.051267 \\ 0.051267 \\ 0.093376 \\ 0.093376 \\ 0.250042 \\ 0.250042 \\ 0.074431 \\ 0.027949 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.014004 \\ 0.023793 \\ 0.023793 \\ 0.038306 \\ 0.038306 \\ 0.038938 \\ 0.038938 \\ 0.040443 \\ 0.040443 \\ 0.040395 \\ 0.040395 \\ 0.05389 \\ 0.05389 \\ 0.062776 \\ 0.063789 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013584 \\ 0.057357 \\ 0.216387 \\ 0.026803 \\ 0.025377 \\ 0.030458 \\ 0.028454 \\ 0.019902 \\ 0.066573 \\ 0.019578 \\ 0.084479 \\ 0.079564 \\ 0.300166 \\ 0.072054 \\ 0.027043 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.007113 \\ -0.016637 \\ -0.016637 \\ -0.019673 \\ -0.019673 \\ -0.019833 \\ -0.019833 \\ -0.020475 \\ -0.020475 \\ -0.020499 \\ -0.020499 \\ -0.023191 \\ -0.023191 \\ -0.032373 \\ -0.032979 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013683 \\ 0.003439 \\ -0.155496 \\ 0.027842 \\ 0.026776 \\ 0.031809 \\ 0.02935 \\ -0.013596 \\ -0.033508 \\ 0.029788 \\ -0.098352 \\ 0.009298 \\ -0.218587 \\ 0.074068 \\ 0.028476 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.667359 \\ -0.667359 \\ 0.005326 \\ -0.005326 \\ 0.014185 \\ -0.014185 \\ 0.657265 \\ -0.657265 \\ 0.67763 \\ -0.67763 \\ 0.667529 \\ -0.667529 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.057418 \\ 0.03745 \\ 0.010278 \\ 0.01057 \\ 0.008618 \\ 0.009485 \\ -0.016204 \\ 0.013158 \\ -0.028355 \\ 0.005887 \\ -0.081247 \\ 0.058358 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000124 \\ 0.009193 \\ 0.009193 \\ 0.000344 \\ 0.000344 \\ 0.000006 \\ 0.000006 \\ 0.000334 \\ 0.000334 \\ 0.000235 \\ 0.000235 \\ 0.009015 \\ 0.009015 \\ 0.000087 \\ 0.000045 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013683 \\ 0.003439 \\ 0.155496 \\ 0.027842 \\ 0.026776 \\ 0.031809 \\ 0.02935 \\ 0.013596 \\ 0.033508 \\ 0.029788 \\ 0.098352 \\ 0.009298 \\ 0.218587 \\ 0.074068 \\ 0.028476 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.000164 \\ 0.000164 \\ 0.003369 \\ 0.003369 \\ 0.003364 \\ 0.003364 \\ 0.00027 \\ 0.00027 \\ 0.000118 \\ 0.000118 \\ 0.000005 \\ 0.000005 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.057418 \\ 0.03745 \\ 0.010278 \\ 0.01057 \\ 0.008618 \\ 0.009485 \\ 0.016204 \\ 0.013158 \\ 0.028355 \\ 0.005887 \\ 0.081247 \\ 0.058358 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | $ \begin{pmatrix} 1 \\ 0.993801 \\ 0.981702 \\ 0.980332e^{i0.981\pi} \\ 0.980332e^{-i0.981\pi} \\ 0.977851e^{i0.984\pi} \\ 0.977851e^{-i0.984\pi} \\ 0.975741 \\ 0.97126e^{i0.031\pi} \\ 0.97126e^{-i0.031\pi} \\ 0.963254e^{i0.031\pi} \\ 0.963254e^{-i0.031\pi} \\ 0.960549e^{i0.951\pi} \\ 0.960549e^{-i0.951\pi} \\ 0.960221e^{i0.986\pi} \\ 0.960221e^{-i0.986\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009384 \\ 0.015198 \\ 0.041006e^{i0.350\pi} \\ 0.041006e^{i0.350\pi} \\ 0.05084e^{i0.287\pi} \\ 0.05084e^{i0.287\pi} \\ 0.025624 \\ 0.096579e^{i0.244\pi} \\ 0.096579e^{i0.244\pi} \\ 0.181851e^{i0.341\pi} \\ 0.181851e^{i0.341\pi} \\ 0.119732e^{i0.121\pi} \\ 0.119732e^{i0.121\pi} \\ 0.123037e^{i0.258\pi} \\ 0.123037e^{i0.258\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.994588 \\ 0.980499 \\ 0.960182e^{i0.980\pi} \\ 0.960182e^{-i0.980\pi} \\ 0.979408e^{i0.984\pi} \\ 0.979408e^{-i0.984\pi} \\ 0.976931 \\ 0.966525e^{i0.028\pi} \\ 0.966525e^{-i0.028\pi} \\ 0.967364e^{i0.035\pi} \\ 0.967364e^{-i0.035\pi} \\ 0.960169e^{i0.957\pi} \\ 0.960169e^{-i0.957\pi} \\ 0.979434e^{i0.993\pi} \\ 0.979434e^{-i0.993\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000788 \\ 0.001203 \\ 0.020181 \\ 0.020181 \\ 0.001585 \\ 0.001585 \\ 0.00119 \\ 0.011886 \\ 0.011886 \\ 0.01072 \\ 0.01072 \\ 0.018967 \\ 0.018967 \\ 0.027763 \\ 0.027763 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009384 \\ 0.015198 \\ 0.041006 \\ 0.041006 \\ 0.05084 \\ 0.05084 \\ 0.025624 \\ 0.096579 \\ 0.096579 \\ 0.181851 \\ 0.181851 \\ 0.119732 \\ 0.119732 \\ 0.123037 \\ 0.123037 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.011577 \\ 0.037442 \\ 0.058703 \\ 0.058703 \\ 0.042286 \\ 0.042286 \\ 0.046769 \\ 0.061312 \\ 0.061312 \\ 0.068231 \\ 0.068231 \\ 0.077891 \\ 0.077891 \\ 0.059727 \\ 0.059727 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009333 \\ 0.014901 \\ 0.016732 \\ 0.018952 \\ 0.02935 \\ 0.032381 \\ 0.025033 \\ 0.072819 \\ 0.061118 \\ 0.09267 \\ 0.074382 \\ 0.091491 \\ 0.120014 \\ 0.081089 \\ 0.084875 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.006219 \\ -0.018468 \\ -0.019864 \\ -0.019864 \\ -0.022398 \\ -0.022398 \\ -0.024558 \\ -0.029161 \\ -0.029161 \\ -0.037438 \\ -0.037438 \\ -0.04025 \\ -0.04025 \\ -0.040591 \\ -0.040591 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009398 \\ 0.015362 \\ -0.016065 \\ -0.020779 \\ -0.029731 \\ -0.03402 \\ 0.025922 \\ 0.076776 \\ 0.065014 \\ 0.1107 \\ 0.083771 \\ -0.1109 \\ -0.128959 \\ -0.082352 \\ -0.091964 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.980585 \\ -0.980585 \\ 0.984285 \\ -0.984285 \\ 0 \\ 0.031318 \\ -0.031318 \\ 0.031442 \\ -0.031442 \\ 0.951046 \\ -0.951046 \\ 0.986162 \\ -0.986162 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.01241 \\ -0.011716 \\ -0.013879 \\ -0.012888 \\ 0 \\ 0.018176 \\ 0.022596 \\ 0.044645 \\ 0.051139 \\ -0.022621 \\ -0.01018 \\ -0.033464 \\ 1.968903 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000792 \\ 0.001226 \\ 0.020768 \\ 0.020768 \\ 0.001591 \\ 0.001591 \\ 0.001219 \\ 0.004888 \\ 0.004888 \\ 0.004258 \\ 0.004258 \\ 0.000396 \\ 0.000396 \\ 0.019811 \\ 0.019811 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009398 \\ 0.015362 \\ 0.016065 \\ 0.020779 \\ 0.029731 \\ 0.03402 \\ 0.025922 \\ 0.076776 \\ 0.065014 \\ 0.1107 \\ 0.083771 \\ 0.1109 \\ 0.128959 \\ 0.082352 \\ 0.091964 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.000369 \\ 0.000369 \\ 0.000097 \\ 0.000097 \\ 0 \\ 0.003582 \\ 0.003582 \\ 0.003265 \\ 0.003265 \\ 0.006285 \\ 0.006285 \\ 0.006578 \\ 0.006578 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.01241 \\ 0.011716 \\ 0.013879 \\ 0.012888 \\ 0 \\ 0.018176 \\ 0.022596 \\ 0.044645 \\ 0.051139 \\ 0.022621 \\ 0.01018 \\ 0.033464 \\ 1.968903 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.987625 \\ -0.986755 \\ -0.985637 \\ 0.971103e^{i0.002\pi} \\ 0.971103e^{-i0.002\pi} \\ 0.970932e^{i0.013\pi} \\ 0.970932e^{-i0.013\pi} \\ 0.970364e^{i0.991\pi} \\ 0.970364e^{-i0.991\pi} \\ 0.970119e^{i0.991\pi} \\ 0.970119e^{-i0.991\pi} \\ -0.957703 \\ -0.956146 \\ 0.954285 \\ 0.949718 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01336 \\ 0.032562 \\ 0.093503 \\ 0.115304e^{i0.422\pi} \\ 0.115304e^{i0.422\pi} \\ 0.046487e^{i0.290\pi} \\ 0.046487e^{i0.290\pi} \\ 0.089213e^{i0.207\pi} \\ 0.089213e^{i0.207\pi} \\ 0.096231e^{i0.273\pi} \\ 0.096231e^{i0.273\pi} \\ 0.122689 \\ 0.085182 \\ 0.097398 \\ 0.019119 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.988623 \\ -0.988673 \\ -0.990931 \\ 0.972595e^{i0.008\pi} \\ 0.972595e^{-i0.008\pi} \\ 0.969888e^{i0.010\pi} \\ 0.969888e^{-i0.010\pi} \\ 0.969933e^{i0.990\pi} \\ 0.969933e^{-i0.990\pi} \\ 0.970133e^{i0.991\pi} \\ 0.970133e^{-i0.991\pi} \\ -0.953677 \\ -0.952676 \\ 0.95332 \\ 0.950183 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.001917 \\ 0.005294 \\ 0.018472 \\ 0.018472 \\ 0.011688 \\ 0.011688 \\ 0.000687 \\ 0.000687 \\ 0.000505 \\ 0.000505 \\ 0.004025 \\ 0.00347 \\ 0.000965 \\ 0.000466 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01336 \\ 0.032562 \\ 0.093503 \\ 0.115304 \\ 0.115304 \\ 0.046487 \\ 0.046487 \\ 0.089213 \\ 0.089213 \\ 0.096231 \\ 0.096231 \\ 0.122689 \\ 0.085182 \\ 0.097398 \\ 0.019119 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.023611 \\ 0.024422 \\ 0.023301 \\ 0.055679 \\ 0.055679 \\ 0.058372 \\ 0.058372 \\ 0.058812 \\ 0.058812 \\ 0.058856 \\ 0.058856 \\ 0.086661 \\ 0.089103 \\ 0.090262 \\ 0.097594 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013208 \\ 0.032194 \\ 0.092655 \\ 0.027797 \\ 0.026449 \\ 0.0285 \\ 0.026845 \\ 0.066823 \\ 0.070957 \\ 0.059344 \\ 0.062866 \\ 0.117005 \\ 0.081151 \\ 0.092851 \\ 0.018166 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.012452 \\ -0.013333 \\ -0.014467 \\ -0.029322 \\ -0.029322 \\ -0.029499 \\ -0.029499 \\ -0.030084 \\ -0.030084 \\ -0.030337 \\ -0.030337 \\ -0.043218 \\ -0.044845 \\ -0.046793 \\ -0.051591 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013437 \\ -0.033556 \\ -0.099672 \\ 0.035186 \\ 0.033918 \\ 0.031113 \\ 0.02813 \\ -0.07232 \\ -0.076117 \\ -0.061521 \\ -0.066341 \\ -0.137089 \\ -0.093311 \\ 0.097184 \\ 0.019931 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 1 \\ 0.001876 \\ -0.001876 \\ 0.013334 \\ -0.013334 \\ 0.990628 \\ -0.990628 \\ 0.990994 \\ -0.990994 \\ 1 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.035424 \\ 0.035574 \\ 0.011273 \\ 0.012069 \\ -0.019764 \\ 1.981644 \\ -0.026019 \\ 1.975109 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.00101 \\ 0.001941 \\ 0.005357 \\ 0.001535 \\ 0.001535 \\ 0.001076 \\ 0.001076 \\ 0.000444 \\ 0.000444 \\ 0.000015 \\ 0.000015 \\ 0.004212 \\ 0.003636 \\ 0.001012 \\ 0.00049 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013437 \\ 0.033556 \\ 0.099672 \\ 0.035186 \\ 0.033918 \\ 0.031113 \\ 0.02813 \\ 0.07232 \\ 0.076117 \\ 0.061521 \\ 0.066341 \\ 0.137089 \\ 0.093311 \\ 0.097184 \\ 0.019931 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.00603 \\ 0.00603 \\ 0.003819 \\ 0.003819 \\ 0.000176 \\ 0.000176 \\ 0.000165 \\ 0.000165 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.035424 \\ 0.035574 \\ 0.011273 \\ 0.012069 \\ 0.019764 \\ 1.981644 \\ 0.026019 \\ 1.975109 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | $ \begin{pmatrix} 1 \\ 0.996204 \\ 0.980007 \\ 0.979024e^{i0.642\pi} \\ 0.979024e^{-i0.642\pi} \\ 0.978377 \\ 0.978299e^{i0.661\pi} \\ 0.978299e^{-i0.661\pi} \\ 0.944858e^{i0.851\pi} \\ 0.944858e^{-i0.851\pi} \\ 0.944852e^{i0.154\pi} \\ 0.944852e^{-i0.154\pi} \\ 0.941714e^{i0.488\pi} \\ 0.941714e^{-i0.488\pi} \\ 0.941446e^{i0.507\pi} \\ 0.941446e^{-i0.507\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007263 \\ 0.036656 \\ 0.027412e^{i0.265\pi} \\ 0.027412e^{i0.265\pi} \\ 0.074416 \\ 0.024584e^{i0.222\pi} \\ 0.024584e^{i0.222\pi} \\ 0.101131e^{i0.342\pi} \\ 0.101131e^{i0.342\pi} \\ 0.10711e^{i0.210\pi} \\ 0.10711e^{i0.210\pi} \\ 0.132393e^{i0.096\pi} \\ 0.132393e^{i0.096\pi} \\ 0.13033e^{i0.335\pi} \\ 0.13033e^{i0.335\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.996286 \\ 0.980069 \\ 0.979042e^{i0.652\pi} \\ 0.979042e^{-i0.652\pi} \\ 0.978522 \\ 0.978287e^{i0.661\pi} \\ 0.978287e^{-i0.661\pi} \\ 0.945618e^{i0.846\pi} \\ 0.945618e^{-i0.846\pi} \\ 0.945558e^{i0.159\pi} \\ 0.945558e^{-i0.159\pi} \\ 0.94081e^{i0.493\pi} \\ 0.94081e^{-i0.493\pi} \\ 0.940744e^{i0.502\pi} \\ 0.940744e^{-i0.502\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000082 \\ 0.000063 \\ 0.030008 \\ 0.030008 \\ 0.000145 \\ 0.000032 \\ 0.000032 \\ 0.014074 \\ 0.014074 \\ 0.014987 \\ 0.014987 \\ 0.014852 \\ 0.014852 \\ 0.015742 \\ 0.015742 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007263 \\ 0.036656 \\ 0.027412 \\ 0.027412 \\ 0.074416 \\ 0.024584 \\ 0.024584 \\ 0.101131 \\ 0.101131 \\ 0.10711 \\ 0.10711 \\ 0.132393 \\ 0.132393 \\ 0.13033 \\ 0.13033 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.007496 \\ 0.039525 \\ 0.041944 \\ 0.041944 \\ 0.042637 \\ 0.042943 \\ 0.042943 \\ 0.106625 \\ 0.106625 \\ 0.106699 \\ 0.106699 \\ 0.114136 \\ 0.114136 \\ 0.114464 \\ 0.114464 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007236 \\ 0.035926 \\ 0.007771 \\ 0.024377 \\ 0.072818 \\ 0.007158 \\ 0.025066 \\ 0.01915 \\ 0.061688 \\ 0.108603 \\ 0.031905 \\ 0.121467 \\ 0.116325 \\ 0.060337 \\ 0.06111 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.003804 \\ -0.020196 \\ -0.021199 \\ -0.021199 \\ -0.021861 \\ -0.02194 \\ -0.02194 \\ -0.056721 \\ -0.056721 \\ -0.056727 \\ -0.056727 \\ -0.060054 \\ -0.060054 \\ -0.060339 \\ -0.060339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007264 \\ 0.036721 \\ 0.010786 \\ -0.027132 \\ 0.073307 \\ 0.005044 \\ -0.023701 \\ 0.002683 \\ -0.090051 \\ 0.105974 \\ 0.050755 \\ 0.053682 \\ -0.027624 \\ 0.114151 \\ -0.1271 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.642018 \\ -0.642018 \\ 0 \\ 0.661452 \\ -0.661452 \\ 0.850543 \\ -0.850543 \\ 0.154005 \\ -0.154005 \\ 0.488105 \\ -0.488105 \\ 0.507344 \\ -0.507344 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.008173 \\ 0.00265 \\ 0 \\ -0.007816 \\ 0.002932 \\ -0.03403 \\ -0.021168 \\ 0.005674 \\ 0.031263 \\ -0.0401 \\ 0.044549 \\ -0.020267 \\ 0.023795 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000083 \\ 0.000064 \\ 0.000018 \\ 0.000018 \\ 0.000149 \\ 0.000012 \\ 0.000012 \\ 0.000804 \\ 0.000804 \\ 0.000747 \\ 0.000747 \\ 0.00096 \\ 0.00096 \\ 0.000745 \\ 0.000745 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007264 \\ 0.036721 \\ 0.010786 \\ 0.027132 \\ 0.073307 \\ 0.005044 \\ 0.023701 \\ 0.002683 \\ 0.090051 \\ 0.105974 \\ 0.050755 \\ 0.053682 \\ 0.027624 \\ 0.114151 \\ 0.1271 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.009757 \\ 0.009757 \\ 0 \\ 0.00001 \\ 0.00001 \\ 0.004733 \\ 0.004733 \\ 0.005042 \\ 0.005042 \\ 0.005013 \\ 0.005013 \\ 0.005319 \\ 0.005319 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.008173 \\ 0.00265 \\ 0 \\ 0.007816 \\ 0.002932 \\ 0.03403 \\ 0.021168 \\ 0.005674 \\ 0.031263 \\ 0.0401 \\ 0.044549 \\ 0.020267 \\ 0.023795 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | $ \begin{pmatrix} 1 \\ -0.975347 \\ 0.971858 \\ 0.968044e^{i0.510\pi} \\ 0.968044e^{-i0.510\pi} \\ 0.955358e^{i0.995\pi} \\ 0.955358e^{-i0.995\pi} \\ 0.954506e^{i0.495\pi} \\ 0.954506e^{-i0.495\pi} \\ 0.95308e^{i0.485\pi} \\ 0.95308e^{-i0.485\pi} \\ -0.950571 \\ 0.942455 \\ 0.938749e^{i0.510\pi} \\ 0.938749e^{-i0.510\pi} \\ 0.936924 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.047724 \\ 0.023799 \\ 0.030164e^{i0.308\pi} \\ 0.030164e^{i0.308\pi} \\ 0.098671e^{i0.284\pi} \\ 0.098671e^{i0.284\pi} \\ 0.113676e^{i0.251\pi} \\ 0.113676e^{i0.251\pi} \\ 0.129189e^{i0.350\pi} \\ 0.129189e^{i0.350\pi} \\ 0.064128 \\ 0.063334 \\ 0.079943e^{i0.172\pi} \\ 0.079943e^{i0.172\pi} \\ 0.092384 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -0.983764 \\ 0.971332 \\ 0.964042e^{i0.513\pi} \\ 0.964042e^{-i0.513\pi} \\ 0.958213e^{i0.996\pi} \\ 0.958213e^{-i0.996\pi} \\ 0.963337e^{i0.487\pi} \\ 0.963337e^{-i0.487\pi} \\ 0.944052e^{i0.487\pi} \\ 0.944052e^{-i0.487\pi} \\ -0.936803 \\ 0.942348 \\ 0.943347e^{i0.513\pi} \\ 0.943347e^{-i0.513\pi} \\ 0.936748 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.008418 \\ 0.000526 \\ 0.009928 \\ 0.009928 \\ 0.003947 \\ 0.003947 \\ 0.023895 \\ 0.023895 \\ 0.010644 \\ 0.010644 \\ 0.013768 \\ 0.000107 \\ 0.008655 \\ 0.008655 \\ 0.000176 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.047724 \\ 0.023799 \\ 0.030164 \\ 0.030164 \\ 0.098671 \\ 0.098671 \\ 0.113676 \\ 0.113676 \\ 0.129189 \\ 0.129189 \\ 0.064128 \\ 0.063334 \\ 0.079943 \\ 0.079943 \\ 0.092384 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.040489 \\ 0.056003 \\ 0.066806 \\ 0.066806 \\ 0.084567 \\ 0.084567 \\ 0.080735 \\ 0.080735 \\ 0.100258 \\ 0.100258 \\ 0.109502 \\ 0.111879 \\ 0.114461 \\ 0.114461 \\ 0.122339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.046949 \\ 0.023117 \\ 0.015762 \\ 0.017133 \\ 0.058638 \\ 0.060169 \\ 0.080263 \\ 0.074081 \\ 0.057699 \\ 0.053052 \\ 0.060075 \\ 0.059683 \\ 0.062061 \\ 0.067281 \\ 0.08654 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.024962 \\ -0.028545 \\ -0.032478 \\ -0.032478 \\ -0.04567 \\ -0.04567 \\ -0.046561 \\ -0.046561 \\ -0.048056 \\ -0.048056 \\ -0.050693 \\ -0.059267 \\ -0.063207 \\ -0.063207 \\ -0.065153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.050168 \\ 0.024194 \\ 0.024956 \\ -0.026442 \\ -0.061978 \\ -0.064848 \\ 0.085231 \\ -0.082329 \\ 0.117726 \\ -0.122273 \\ -0.069846 \\ 0.06504 \\ 0.043026 \\ -0.044344 \\ 0.09404 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0.510258 \\ -0.510258 \\ 0.994992 \\ -0.994992 \\ 0.494627 \\ -0.494627 \\ 0.48476 \\ -0.48476 \\ 1 \\ 0 \\ 0.510357 \\ -0.510357 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.005731 \\ 0.005492 \\ -0.027588 \\ 1.973029 \\ -0.024155 \\ 0.029561 \\ -0.015781 \\ 0.024235 \\ 0 \\ 0 \\ -0.022726 \\ 0.023856 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.008593 \\ 0.000542 \\ 0.004142 \\ 0.004142 \\ 0.002985 \\ 0.002985 \\ 0.009209 \\ 0.009209 \\ 0.009517 \\ 0.009517 \\ 0.014589 \\ 0.000113 \\ 0.004885 \\ 0.004885 \\ 0.000188 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.050168 \\ 0.024194 \\ 0.024956 \\ 0.026442 \\ 0.061978 \\ 0.064848 \\ 0.085231 \\ 0.082329 \\ 0.117726 \\ 0.122273 \\ 0.069846 \\ 0.06504 \\ 0.043026 \\ 0.044344 \\ 0.09404 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.002994 \\ 0.002994 \\ 0.000906 \\ 0.000906 \\ 0.007371 \\ 0.007371 \\ 0.001893 \\ 0.001893 \\ 0 \\ 0 \\ 0.00248 \\ 0.00248 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.005731 \\ 0.005492 \\ 0.027588 \\ 1.973029 \\ 0.024155 \\ 0.029561 \\ 0.015781 \\ 0.024235 \\ 0 \\ 0 \\ 0.022726 \\ 0.023856 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 0.971349 \\ 0.947583e^{i0.989\pi} \\ 0.947583e^{-i0.989\pi} \\ 0.944802e^{i0.974\pi} \\ 0.944802e^{-i0.974\pi} \\ 0.943618e^{i0.960\pi} \\ 0.943618e^{-i0.960\pi} \\ 0.94338e^{i0.987\pi} \\ 0.94338e^{-i0.987\pi} \\ 0.941212 \\ 0.932826e^{i0.021\pi} \\ 0.932826e^{-i0.021\pi} \\ 0.930681e^{i0.045\pi} \\ 0.930681e^{-i0.045\pi} \\ 0.926425 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039865 \\ 0.409134e^{i0.330\pi} \\ 0.409134e^{i0.330\pi} \\ 0.07032e^{i0.111\pi} \\ 0.07032e^{i0.111\pi} \\ 0.166584e^{i0.464\pi} \\ 0.166584e^{i0.464\pi} \\ 0.511003e^{i0.394\pi} \\ 0.511003e^{i0.394\pi} \\ 0.04533 \\ 0.148045e^{i0.355\pi} \\ 0.148045e^{i0.355\pi} \\ 0.127488e^{i0.233\pi} \\ 0.127488e^{i0.233\pi} \\ 0.163061 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.973291 \\ 0.968023e^{i0.988\pi} \\ 0.968023e^{-i0.988\pi} \\ 0.950772e^{i0.974\pi} \\ 0.950772e^{-i0.974\pi} \\ 0.937273e^{i0.974\pi} \\ 0.937273e^{-i0.974\pi} \\ 0.923674e^{i0.988\pi} \\ 0.923674e^{-i0.988\pi} \\ 0.939531 \\ 0.932266e^{i0.014\pi} \\ 0.932266e^{-i0.014\pi} \\ 0.930983e^{i0.039\pi} \\ 0.930983e^{-i0.039\pi} \\ 0.927143 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001942 \\ 0.020893 \\ 0.020893 \\ 0.005982 \\ 0.005982 \\ 0.040059 \\ 0.040059 \\ 0.019824 \\ 0.019824 \\ 0.001681 \\ 0.022088 \\ 0.022088 \\ 0.018857 \\ 0.018857 \\ 0.000718 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039865 \\ 0.409134 \\ 0.409134 \\ 0.07032 \\ 0.07032 \\ 0.166584 \\ 0.166584 \\ 0.511003 \\ 0.511003 \\ 0.04533 \\ 0.148045 \\ 0.148045 \\ 0.127488 \\ 0.127488 \\ 0.163061 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.054594 \\ 0.082727 \\ 0.082727 \\ 0.101709 \\ 0.101709 \\ 0.116354 \\ 0.116354 \\ 0.128627 \\ 0.128627 \\ 0.115703 \\ 0.130602 \\ 0.130602 \\ 0.13373 \\ 0.13373 \\ 0.141072 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.038801 \\ 0.194059 \\ 0.20982 \\ 0.057521 \\ 0.067738 \\ 0.01594 \\ 0.018798 \\ 0.148 \\ 0.160066 \\ 0.042589 \\ 0.063259 \\ 0.058004 \\ 0.098261 \\ 0.076934 \\ 0.151181 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.029069 \\ -0.053841 \\ -0.053841 \\ -0.05678 \\ -0.05678 \\ -0.058033 \\ -0.058033 \\ -0.058286 \\ -0.058286 \\ -0.060587 \\ -0.069537 \\ -0.069537 \\ -0.071839 \\ -0.071839 \\ -0.076422 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.040221 \\ -0.129608 \\ -0.163945 \\ -0.069484 \\ -0.07428 \\ 0.017449 \\ -0.026381 \\ -0.008904 \\ -0.054096 \\ 0.047037 \\ 0.08425 \\ 0.067861 \\ 0.110066 \\ 0.088907 \\ 0.162128 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.989022 \\ -0.989022 \\ 0.973965 \\ -0.973965 \\ 0.960477 \\ -0.960477 \\ 0.986801 \\ -0.986801 \\ 0 \\ 0.021323 \\ -0.021323 \\ 0.045006 \\ -0.045006 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.141877 \\ 1.859124 \\ -0.010597 \\ -0.006728 \\ -0.055498 \\ 1.943609 \\ -0.175376 \\ 1.821357 \\ 0 \\ 0.040353 \\ 0.043827 \\ 0.021785 \\ 0.03064 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.001997 \\ 0.021342 \\ 0.021342 \\ 0.006299 \\ 0.006299 \\ 0.006747 \\ 0.006747 \\ 0.02111 \\ 0.02111 \\ 0.001788 \\ 0.0006 \\ 0.0006 \\ 0.000324 \\ 0.000324 \\ 0.000774 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.040221 \\ 0.129608 \\ 0.163945 \\ 0.069484 \\ 0.07428 \\ 0.017449 \\ 0.026381 \\ 0.008904 \\ 0.054096 \\ 0.047037 \\ 0.08425 \\ 0.067861 \\ 0.110066 \\ 0.088907 \\ 0.162128 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.001438 \\ 0.001438 \\ 0.000129 \\ 0.000129 \\ 0.013389 \\ 0.013389 \\ 0.000738 \\ 0.000738 \\ 0 \\ 0.007537 \\ 0.007537 \\ 0.006448 \\ 0.006448 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.141877 \\ 1.859124 \\ 0.010597 \\ 0.006728 \\ 0.055498 \\ 1.943609 \\ 0.175376 \\ 1.821357 \\ 0 \\ 0.040353 \\ 0.043827 \\ 0.021785 \\ 0.03064 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | $ \begin{pmatrix} 1 \\ 0.970663e^{i0.669\pi} \\ 0.970663e^{-i0.669\pi} \\ 0.969071 \\ 0.941329 \\ 0.939664e^{i0.688\pi} \\ 0.939664e^{-i0.688\pi} \\ 0.932257e^{i0.688\pi} \\ 0.932257e^{-i0.688\pi} \\ 0.932138e^{i0.669\pi} \\ 0.932138e^{-i0.669\pi} \\ 0.931944 \\ 0.930898e^{i0.019\pi} \\ 0.930898e^{-i0.019\pi} \\ 0.930232e^{i0.642\pi} \\ 0.930232e^{-i0.642\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.024124e^{i0.230\pi} \\ 0.024124e^{i0.230\pi} \\ 0.042048 \\ 0.071238 \\ 0.048131e^{i0.264\pi} \\ 0.048131e^{i0.264\pi} \\ 0.135985e^{i0.193\pi} \\ 0.135985e^{i0.193\pi} \\ 0.15567e^{i0.184\pi} \\ 0.15567e^{i0.184\pi} \\ 0.048012 \\ 0.122574e^{i0.273\pi} \\ 0.122574e^{i0.273\pi} \\ 0.217404e^{i0.073\pi} \\ 0.217404e^{i0.073\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.970418e^{i0.670\pi} \\ 0.970418e^{-i0.670\pi} \\ 0.971191 \\ 0.941055 \\ 0.939438e^{i0.683\pi} \\ 0.939438e^{-i0.683\pi} \\ 0.932687e^{i0.683\pi} \\ 0.932687e^{-i0.683\pi} \\ 0.931416e^{i0.670\pi} \\ 0.931416e^{-i0.670\pi} \\ 0.931273 \\ 0.931155e^{i0.013\pi} \\ 0.931155e^{-i0.013\pi} \\ 0.930181e^{i0.647\pi} \\ 0.930181e^{-i0.647\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.001078 \\ 0.001078 \\ 0.00212 \\ 0.000274 \\ 0.016402 \\ 0.016402 \\ 0.015185 \\ 0.015185 \\ 0.001256 \\ 0.001256 \\ 0.00067 \\ 0.017076 \\ 0.017076 \\ 0.014606 \\ 0.014606 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.024124 \\ 0.024124 \\ 0.042048 \\ 0.071238 \\ 0.048131 \\ 0.048131 \\ 0.135985 \\ 0.135985 \\ 0.15567 \\ 0.15567 \\ 0.048012 \\ 0.122574 \\ 0.122574 \\ 0.217404 \\ 0.217404 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.058052 \\ 0.058052 \\ 0.058847 \\ 0.114157 \\ 0.117378 \\ 0.117378 \\ 0.130612 \\ 0.130612 \\ 0.131792 \\ 0.131792 \\ 0.132106 \\ 0.133335 \\ 0.133335 \\ 0.134822 \\ 0.134822 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006193 \\ 0.024064 \\ 0.040837 \\ 0.067039 \\ 0.009034 \\ 0.042207 \\ 0.030739 \\ 0.144067 \\ 0.042871 \\ 0.166165 \\ 0.044712 \\ 0.077705 \\ 0.071506 \\ 0.088286 \\ 0.264057 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.029776 \\ -0.029776 \\ -0.031417 \\ -0.060463 \\ -0.062233 \\ -0.062233 \\ -0.070147 \\ -0.070147 \\ -0.070274 \\ -0.070274 \\ -0.070483 \\ -0.071605 \\ -0.071605 \\ -0.072321 \\ -0.072321 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.004966 \\ -0.023871 \\ 0.042475 \\ 0.072951 \\ 0.013204 \\ -0.05195 \\ 0.012762 \\ -0.144164 \\ 0.021397 \\ -0.158336 \\ 0.050235 \\ 0.091674 \\ 0.081655 \\ -0.02344 \\ -0.136164 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.669479 \\ -0.669479 \\ 0 \\ 0 \\ 0.688437 \\ -0.688437 \\ 0.688269 \\ -0.688269 \\ 0.669276 \\ -0.669276 \\ 0 \\ 0.019055 \\ -0.019055 \\ 0.642295 \\ -0.642295 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.007732 \\ 0.002521 \\ 0 \\ 0 \\ -0.015644 \\ 0.002549 \\ -0.045996 \\ 0.019515 \\ -0.052209 \\ 0.027671 \\ 0 \\ 0.027407 \\ 0.03072 \\ -0.075072 \\ 0.066906 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.000253 \\ 0.000253 \\ 0.002185 \\ 0.000291 \\ 0.00024 \\ 0.00024 \\ 0.000461 \\ 0.000461 \\ 0.000775 \\ 0.000775 \\ 0.00072 \\ 0.000275 \\ 0.000275 \\ 0.000054 \\ 0.000054 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.004966 \\ 0.023871 \\ 0.042475 \\ 0.072951 \\ 0.013204 \\ 0.05195 \\ 0.012762 \\ 0.144164 \\ 0.021397 \\ 0.158336 \\ 0.050235 \\ 0.091674 \\ 0.081655 \\ 0.02344 \\ 0.136164 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000344 \\ 0.000344 \\ 0 \\ 0 \\ 0.005556 \\ 0.005556 \\ 0.005182 \\ 0.005182 \\ 0.000351 \\ 0.000351 \\ 0 \\ 0.005838 \\ 0.005838 \\ 0.004998 \\ 0.004998 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.007732 \\ 0.002521 \\ 0 \\ 0 \\ 0.015644 \\ 0.002549 \\ 0.045996 \\ 0.019515 \\ 0.052209 \\ 0.027671 \\ 0 \\ 0.027407 \\ 0.03072 \\ 0.075072 \\ 0.066906 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 0.932375e^{i0.988\pi} \\ 0.932375e^{-i0.988\pi} \\ 0.93171 \\ 0.930714e^{i0.986\pi} \\ 0.930714e^{-i0.986\pi} \\ 0.927195 \\ 0.92616 \\ 0.924552e^{i0.970\pi} \\ 0.924552e^{-i0.970\pi} \\ 0.92371e^{i0.996\pi} \\ 0.92371e^{-i0.996\pi} \\ 0.922909e^{i0.017\pi} \\ 0.922909e^{-i0.017\pi} \\ 0.904111e^{i0.013\pi} \\ 0.904111e^{-i0.013\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.089475e^{i0.357\pi} \\ 0.089475e^{i0.357\pi} \\ 0.16213 \\ 0.147497e^{i0.306\pi} \\ 0.147497e^{i0.306\pi} \\ 0.109491 \\ 0.179819 \\ 0.102025e^{i0.101\pi} \\ 0.102025e^{i0.101\pi} \\ 0.162522e^{i0.242\pi} \\ 0.162522e^{i0.242\pi} \\ 0.208149e^{i0.221\pi} \\ 0.208149e^{i0.221\pi} \\ 0.236978e^{i0.353\pi} \\ 0.236978e^{i0.353\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.926639e^{i0.996\pi} \\ -0.931373 \\ 0.930378e^{-i0.001\pi} \\ 0.925963e^{i0.990\pi} \\ 0.925963e^{-i0.990\pi} \\ 0.927525 \\ 0.923571 \\ 0.928311e^{i0.986\pi} \\ 0.928311e^{-i0.986\pi} \\ -0.925817 \\ 0.926639e^{-i0.996\pi} \\ 0.925509e^{i0.009\pi} \\ 0.925509e^{-i0.009\pi} \\ 0.930378e^{i0.001\pi} \\ 0.880493 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.024383 \\ 0.03412 \\ 0.00389 \\ 0.011825 \\ 0.011825 \\ 0.00033 \\ 0.002589 \\ 0.046114 \\ 0.046114 \\ 0.011529 \\ 0.003117 \\ 0.023205 \\ 0.023205 \\ 0.043076 \\ 0.043655 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.089475 \\ 0.089475 \\ 0.16213 \\ 0.147497 \\ 0.147497 \\ 0.109491 \\ 0.179819 \\ 0.102025 \\ 0.102025 \\ 0.162522 \\ 0.162522 \\ 0.208149 \\ 0.208149 \\ 0.236978 \\ 0.236978 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.136306 \\ 0.132192 \\ 0.133164 \\ 0.138252 \\ 0.138252 \\ 0.140003 \\ 0.144626 \\ 0.142784 \\ 0.142784 \\ 0.144878 \\ 0.144055 \\ 0.146105 \\ 0.146105 \\ 0.159418 \\ 0.20461 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.03556 \\ 0.036145 \\ 0.150249 \\ 0.075464 \\ 0.080532 \\ 0.101555 \\ 0.166076 \\ 0.085911 \\ 0.093841 \\ 0.109119 \\ 0.110421 \\ 0.152181 \\ 0.143798 \\ 0.09837 \\ 0.092732 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.07002 \\ -0.07002 \\ -0.070733 \\ -0.071803 \\ -0.071803 \\ -0.075591 \\ -0.076708 \\ -0.078446 \\ -0.078446 \\ -0.079358 \\ -0.079358 \\ -0.080225 \\ -0.080225 \\ -0.100803 \\ -0.100803 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.035025 \\ -0.041859 \\ 0.160428 \\ -0.077939 \\ -0.091537 \\ 0.11162 \\ 0.17744 \\ -0.105413 \\ -0.113449 \\ -0.125031 \\ -0.128859 \\ 0.172643 \\ 0.161644 \\ 0.139119 \\ 0.124274 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.98835 \\ -0.98835 \\ 0 \\ 0.985949 \\ -0.985949 \\ 0 \\ 0 \\ 0.970175 \\ -0.970175 \\ 0.996098 \\ -0.996098 \\ 0.016955 \\ -0.016955 \\ 0.013099 \\ -0.013099 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.029028 \\ 1.971787 \\ 0 \\ -0.046249 \\ 1.95593 \\ 0 \\ 0 \\ -0.015624 \\ -0.008752 \\ -0.044402 \\ 1.95657 \\ 0.036202 \\ 0.04164 \\ 0.064083 \\ 0.067809 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.006171 \\ 0.001075 \\ 0.001431 \\ 0.005118 \\ 0.005118 \\ 0.000355 \\ 0.0028 \\ 0.004058 \\ 0.004058 \\ 0.002279 \\ 0.003166 \\ 0.002813 \\ 0.002813 \\ 0.028639 \\ 0.02647 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.035025 \\ 0.041859 \\ 0.160428 \\ 0.077939 \\ 0.091537 \\ 0.11162 \\ 0.17744 \\ 0.105413 \\ 0.113449 \\ 0.125031 \\ 0.128859 \\ 0.172643 \\ 0.161644 \\ 0.139119 \\ 0.124274 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.008116 \\ 1.98835 \\ 0.00125 \\ 0.003713 \\ 0.003713 \\ 0 \\ 0 \\ 0.015793 \\ 0.015793 \\ 0.003902 \\ 0.000367 \\ 0.007942 \\ 0.007942 \\ 0.01185 \\ 0.013099 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.029028 \\ 1.971787 \\ 0 \\ 0.046249 \\ 1.95593 \\ 0 \\ 0 \\ 0.015624 \\ 0.008752 \\ 0.044402 \\ 1.95657 \\ 0.036202 \\ 0.04164 \\ 0.064083 \\ 0.067809 \end{pmatrix} $ π |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 0.952616e^{i0.988\pi} \\ 0.952616e^{-i0.988\pi} \\ 0.947962 \\ 0.932724 \\ -0.931957 \\ 0.920405e^{i0.986\pi} \\ 0.920405e^{-i0.986\pi} \\ -0.915728 \\ 0.91507e^{i0.012\pi} \\ 0.91507e^{-i0.012\pi} \\ 0.909273e^{i0.014\pi} \\ 0.909273e^{-i0.014\pi} \\ 0.909227e^{i0.997\pi} \\ 0.909227e^{-i0.997\pi} \\ 0.906751 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.068075e^{i0.265\pi} \\ 0.068075e^{i0.265\pi} \\ 0.058865 \\ 0.080615 \\ 0.116338 \\ 0.216153e^{i0.263\pi} \\ 0.216153e^{i0.263\pi} \\ 0.280259 \\ 0.241891e^{i0.177\pi} \\ 0.241891e^{i0.177\pi} \\ 0.167407e^{i0.216\pi} \\ 0.167407e^{i0.216\pi} \\ 0.403786e^{i0.316\pi} \\ 0.403786e^{i0.316\pi} \\ 0.253563 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0.954813e^{i0.987\pi} \\ 0.954813e^{-i0.987\pi} \\ 0.946742 \\ 0.934716 \\ 0.930421e^{i0.999\pi} \\ 0.916436e^{i0.986\pi} \\ 0.916436e^{-i0.986\pi} \\ 0.930421e^{-i0.999\pi} \\ 0.912841e^{i0.011\pi} \\ 0.912841e^{-i0.011\pi} \\ 0.909862e^{i0.016\pi} \\ 0.909862e^{-i0.016\pi} \\ 0.905479e^{i0.997\pi} \\ 0.905479e^{-i0.997\pi} \\ 0.907443 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.003373 \\ 0.003373 \\ 0.00122 \\ 0.001991 \\ 0.004382 \\ 0.004052 \\ 0.004052 \\ 0.015247 \\ 0.00328 \\ 0.00328 \\ 0.004303 \\ 0.004303 \\ 0.00375 \\ 0.00375 \\ 0.000692 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.068075 \\ 0.068075 \\ 0.058865 \\ 0.080615 \\ 0.116338 \\ 0.216153 \\ 0.216153 \\ 0.280259 \\ 0.241891 \\ 0.241891 \\ 0.167407 \\ 0.167407 \\ 0.403786 \\ 0.403786 \\ 0.253563 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.090433 \\ 0.090433 \\ 0.102525 \\ 0.128168 \\ 0.132896 \\ 0.156508 \\ 0.156508 \\ 0.147996 \\ 0.164689 \\ 0.164689 \\ 0.172695 \\ 0.172695 \\ 0.176714 \\ 0.176714 \\ 0.177176 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041938 \\ 0.045573 \\ 0.05573 \\ 0.075352 \\ 0.107765 \\ 0.128204 \\ 0.14034 \\ 0.261905 \\ 0.193991 \\ 0.180499 \\ 0.124343 \\ 0.112461 \\ 0.198319 \\ 0.201586 \\ 0.230094 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ -0.048544 \\ -0.048544 \\ -0.053441 \\ -0.069646 \\ -0.070469 \\ -0.082941 \\ -0.082941 \\ -0.088036 \\ -0.088755 \\ -0.088755 \\ -0.09511 \\ -0.09511 \\ -0.095161 \\ -0.095161 \\ -0.097888 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.045518 \\ -0.05003 \\ 0.060244 \\ 0.082896 \\ -0.13334 \\ -0.142482 \\ -0.163214 \\ -0.365355 \\ 0.212295 \\ 0.205176 \\ 0.142851 \\ 0.134895 \\ -0.165881 \\ -0.174562 \\ 0.246578 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.987637 \\ -0.987637 \\ 0 \\ 0 \\ 1 \\ 0.985905 \\ -0.985905 \\ 1 \\ 0.012301 \\ -0.012301 \\ 0.014466 \\ -0.014466 \\ 0.997356 \\ -0.997356 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.018211 \\ 1.98296 \\ 0 \\ 0 \\ 0 \\ -0.066327 \\ 1.937661 \\ 0 \\ 0.033811 \\ 0.038577 \\ 0.030113 \\ 0.033995 \\ -0.145464 \\ 1.854875 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0.002304 \\ 0.002304 \\ 0.001287 \\ 0.002132 \\ 0.001649 \\ 0.004322 \\ 0.004322 \\ 0.015918 \\ 0.002439 \\ 0.002439 \\ 0.000648 \\ 0.000648 \\ 0.00413 \\ 0.00413 \\ 0.000763 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.045518 \\ 0.05003 \\ 0.060244 \\ 0.082896 \\ 0.13334 \\ 0.142482 \\ 0.163214 \\ 0.365355 \\ 0.212295 \\ 0.205176 \\ 0.142851 \\ 0.134895 \\ 0.165881 \\ 0.174562 \\ 0.246578 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.000854 \\ 0.000854 \\ 0 \\ 0 \\ 0.001403 \\ 0.000281 \\ 0.000281 \\ 1.998597 \\ 0.000838 \\ 0.000838 \\ 0.001492 \\ 0.001492 \\ 0.000044 \\ 0.000044 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018211 \\ 1.98296 \\ 0 \\ 0 \\ 0 \\ 0.066327 \\ 1.937661 \\ 0 \\ 0.033811 \\ 0.038577 \\ 0.030113 \\ 0.033995 \\ 0.145464 \\ 1.854875 \\ 0 \end{pmatrix} $ π |
| Gate or Germ | Eigenvalues ($E$) | Target Evals. ($T$) | $|E - T|$ | $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ | $\mathrm{Re} \log(E)$ | $\mathrm{Im} \log(E)$ | $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ | $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$ |
|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gxpi2:1 | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gxpi2:0 | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gypi2:1 | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gypi2:0 | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Gcphase:0:1 | $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ -1 \\ 0 \\ 1 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | $ \begin{pmatrix} 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.167\pi} \\ 1e^{-i0.167\pi} \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1e^{i0.833\pi} \\ 1e^{-i0.833\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.167\pi} \\ 1e^{-i0.167\pi} \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1e^{i0.833\pi} \\ 1e^{-i0.833\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.166667 \\ -0.166667 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0.833333 \\ -0.833333 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ -1 \\ -1 \\ 1 \\ -1 \\ 1i \\ -1i \\ 1 \\ -1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ -1 \\ -1 \\ 1 \\ -1 \\ 1i \\ -1i \\ 1 \\ -1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0.5 \\ -0.5 \\ 1 \\ -1 \\ 0 \\ 1 \\ 0.5 \\ -0.5 \\ 0 \\ 1 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ -1 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 2 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π |
Gauge Variant Error Metrics
This tab provides a variety of common (and uncommon) error metrics derived from the estimated gate set. All of these quanties are gauge-dependent
, which means two things. First, they aren't directly physically measurable, so they can't map directly to observable error rates. Second, they are only as reliable (as diagnostics) inasmuch as pyGSTi is able to pick a sensible gauge (reference frame) in which to report gates. PyGSTi does this by first finding an estimate based on the data (and ignoring gauge entirely), then varying over all possible representations of those gates (gauges) to minimize a measure of the gates' implausibility (distance from the targets, combined with violation of positivity). This measure has parameters -- e.g. the weights placed on different gates -- and reports often include multiple "gauge optimizations". A dropdown menu in the sidebar allows switching between these options, and the parameters used for the currently-shown estimate are shown below it.
| Prep/POVM | Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist |
|---|---|---|---|
| ρ0 | 0.044929 ± 0.003336 | 0.047612 ± 0.004058 | -- |
| Mdefault | 0.075016 ± 0.001597 | 0.07619 ± 0.001826 | 0.122059 ± 0.004307 |
| Prep/POVM | Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist |
|---|---|---|---|
| ρ0 | 0.063947 ± 0.004108 | 0.076873 ± 0.002123 | -- |
| Mdefault | 0.071503 ± 0.001628 | 0.074579 ± 0.002454 | 0.077766 ± 0.003319 |
| Prep/POVM | Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist |
|---|---|---|---|
| ρ0 | 0 | 0 | -- |
| Mdefault | 0 | 0 | 0 |
| Gate | Entanglement Infidelity | Avg. Gate Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Non-unitary Ent. Infidelity | Non-unitary Avg. Gate Infidelity |
|---|---|---|---|---|---|---|
| [] | 0.004518 ± 0.003354 | 0.003615 ± 0.002683 | 0.008601 ± 0.015255 | 0.010213 ± 0.024067 | 0.004478 ± 0.003236 | 0.003582 ± 0.002589 |
| Gxpi2:1 | 0.004066 ± 0.00333 | 0.003253 ± 0.002664 | 0.008238 ± 0.008764 | 0.011578 ± 0.016654 | 0.004027 ± 0.003333 | 0.003222 ± 0.002667 |
| Gxpi2:0 | 0.00576 ± 0.003517 | 0.004608 ± 0.002813 | 0.020257 ± 0.008829 | 0.027131 ± 0.023717 | 0.005433 ± 0.003517 | 0.004347 ± 0.002813 |
| Gypi2:1 | 0.006353 ± 0.004823 | 0.005083 ± 0.003859 | 0.016997 ± 0.008889 | 0.024357 ± 0.025227 | 0.006157 ± 0.00476 | 0.004925 ± 0.003808 |
| Gypi2:0 | 0.010279 ± 0.004381 | 0.008223 ± 0.003505 | 0.026744 ± 0.011663 | 0.035214 ± 0.044543 | 0.009742 ± 0.004409 | 0.007794 ± 0.003527 |
| Gcphase:0:1 | 0.023373 ± 0.006443 | 0.018699 ± 0.005154 | 0.044264 ± 0.007059 | 0.061999 ± 0.03809 | 0.022268 ± 0.00622 | 0.017814 ± 0.004976 |
| Gate | Entanglement Infidelity | Avg. Gate Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Non-unitary Ent. Infidelity | Non-unitary Avg. Gate Infidelity |
|---|---|---|---|---|---|---|
| [] | 0.008327 ± 0.004118 | 0.006662 ± 0.003294 | 0.013126 ± 0.113007 | 0.015144 ± 0.013637 | 0.008238 ± 0.003836 | 0.00659 ± 0.003069 |
| Gxpi2:1 | 0.009474 ± 0.003728 | 0.007579 ± 0.002983 | 0.01249 ± 0.005867 | 0.014506 ± 0.03951 | 0.009412 ± 0.0037 | 0.007529 ± 0.00296 |
| Gxpi2:0 | 0.008635 ± 0.006525 | 0.006908 ± 0.00522 | 0.026421 ± 0.007359 | 0.034333 ± 0.043641 | 0.008121 ± 0.006309 | 0.006496 ± 0.005047 |
| Gypi2:1 | 0.010377 ± 0.007077 | 0.008302 ± 0.005662 | 0.02524 ± 0.007416 | 0.031271 ± 0.016447 | 0.009964 ± 0.00698 | 0.007972 ± 0.005584 |
| Gypi2:0 | 0.010939 ± 0.005013 | 0.008751 ± 0.004011 | 0.028377 ± 0.016611 | 0.036155 ± 0.002875 | 0.010323 ± 0.004965 | 0.008259 ± 0.003972 |
| Gcphase:0:1 | 0.018755 ± 0.005138 | 0.015004 ± 0.004111 | 0.042103 ± 0.005652 | 0.048942 ± 0.047235 | 0.017644 ± 0.005879 | 0.014115 ± 0.004703 |
| Gate | Entanglement Infidelity | Avg. Gate Infidelity | 1/2 Trace Distance | 1/2 Diamond-Dist | Non-unitary Ent. Infidelity | Non-unitary Avg. Gate Infidelity |
|---|---|---|---|---|---|---|
| [] | 0 | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gxpi2:0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gypi2:0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Entanglement Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.004518 | 0.008327 | 0 |
| Gxpi2:1 | 0.004066 | 0.009474 | 0 |
| Gxpi2:0 | 0.00576 | 0.008635 | 0 |
| Gypi2:1 | 0.006353 | 0.010377 | 0 |
| Gypi2:0 | 0.010279 | 0.010939 | 0 |
| Gcphase:0:1 | 0.023373 | 0.018755 | 0 |
| Avg. Gate Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.003615 | 0.006662 | 0 |
| Gxpi2:1 | 0.003253 | 0.007579 | 0 |
| Gxpi2:0 | 0.004608 | 0.006908 | 0 |
| Gypi2:1 | 0.005083 | 0.008302 | 0 |
| Gypi2:0 | 0.008223 | 0.008751 | 0 |
| Gcphase:0:1 | 0.018699 | 0.015004 | 0 |
| 1/2 Trace Distance | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.008601 | 0.013126 | 0 |
| Gxpi2:1 | 0.008238 | 0.01249 | 0 |
| Gxpi2:0 | 0.020257 | 0.026421 | 0 |
| Gypi2:1 | 0.016997 | 0.02524 | 0 |
| Gypi2:0 | 0.026744 | 0.028377 | 0 |
| Gcphase:0:1 | 0.044264 | 0.042103 | 0 |
| 1/2 Diamond-Dist | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.010213 | 0.015144 | 0 |
| Gxpi2:1 | 0.011578 | 0.014506 | 0 |
| Gxpi2:0 | 0.027131 | 0.034333 | 0 |
| Gypi2:1 | 0.024357 | 0.031271 | 0 |
| Gypi2:0 | 0.035214 | 0.036155 | 0 |
| Gcphase:0:1 | 0.061999 | 0.048942 | 0 |
| Non-unitary Ent. Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.004478 | 0.008238 | 0 |
| Gxpi2:1 | 0.004027 | 0.009412 | 0 |
| Gxpi2:0 | 0.005433 | 0.008121 | 0 |
| Gypi2:1 | 0.006157 | 0.009964 | 0 |
| Gypi2:0 | 0.009742 | 0.010323 | 0 |
| Gcphase:0:1 | 0.022268 | 0.017644 | 0 |
| Non-unitary Avg. Gate Infidelity | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.003582 | 0.00659 | 0 |
| Gxpi2:1 | 0.003222 | 0.007529 | 0 |
| Gxpi2:0 | 0.004347 | 0.006496 | 0 |
| Gypi2:1 | 0.004925 | 0.007972 | 0 |
| Gypi2:0 | 0.007794 | 0.008259 | 0 |
| Gcphase:0:1 | 0.017814 | 0.014115 | 0 |
| Frobenius Distance | |||
|---|---|---|---|
| Gate | CPTP | H+S | Target |
| [] | 0.040828 | 0.063392 | 0 |
| Gxpi2:1 | 0.039346 | 0.05913 | 0 |
| Gxpi2:0 | 0.104727 | 0.132604 | 0 |
| Gypi2:1 | 0.083586 | 0.122105 | 0 |
| Gypi2:0 | 0.137387 | 0.1467 | 0 |
| Gcphase:0:1 | 0.210313 | 0.20214 | 0 |
| Gate or Germ | Entanglement Infidelity | 1/2 Trace Distance | Non-unitary Ent. Infidelity |
|---|---|---|---|
| [] | 0.004518 | 0.008601 | 0.004478 |
| Gxpi2:1 | 0.004066 | 0.008238 | 0.004027 |
| Gxpi2:0 | 0.00576 | 0.020257 | 0.005433 |
| Gypi2:1 | 0.006353 | 0.016997 | 0.006157 |
| Gypi2:0 | 0.010279 | 0.026744 | 0.009742 |
| Gcphase:0:1 | 0.023373 | 0.044264 | 0.022268 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0.016571 | 0.044131 | 0.015105 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0.01041 | 0.021156 | 0.010157 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0.023213 | 0.060877 | 0.020427 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0.014463 | 0.025971 | 0.014133 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0.033965 | 0.059248 | 0.032201 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0.039028 | 0.067595 | 0.036689 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0.037984 | 0.061405 | 0.036312 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0.033819 | 0.048957 | 0.032894 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0.07087 | 0.09574 | 0.067882 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0.053781 | 0.082634 | 0.05079 |
| Gate or Germ | Entanglement Infidelity | 1/2 Trace Distance | Non-unitary Ent. Infidelity |
|---|---|---|---|
| [] | 0.008327 | 0.013126 | 0.008238 |
| Gxpi2:1 | 0.009474 | 0.01249 | 0.009412 |
| Gxpi2:0 | 0.008635 | 0.026421 | 0.008121 |
| Gypi2:1 | 0.010377 | 0.02524 | 0.009964 |
| Gypi2:0 | 0.010939 | 0.028377 | 0.010323 |
| Gcphase:0:1 | 0.018755 | 0.042103 | 0.017644 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0.020104 | 0.049544 | 0.018306 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0.019776 | 0.033747 | 0.019197 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0.029802 | 0.070879 | 0.026249 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0.029018 | 0.04189 | 0.028266 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0.038431 | 0.065043 | 0.036308 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0.044974 | 0.073381 | 0.042437 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0.058372 | 0.093613 | 0.054261 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0.05718 | 0.078431 | 0.054985 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0.073985 | 0.10045 | 0.070663 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0.077538 | 0.117193 | 0.071591 |
| Gate or Germ | Entanglement Infidelity | 1/2 Trace Distance | Non-unitary Ent. Infidelity |
|---|---|---|---|
| [] | 0 | 0 | 0 |
| Gxpi2:1 | 0 | 0 | 0 |
| Gxpi2:0 | 0 | 0 | 0 |
| Gypi2:1 | 0 | 0 | 0 |
| Gypi2:0 | 0 | 0 | 0 |
| Gcphase:0:1 | 0 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- | 0 | 0 | 0 |
| Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- | 0 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- | 0 | 0 | 0 |
| Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- | 0 | 0 | 0 |
| Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- | 0 | 0 | 0 |
| Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- | 0 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- | 0 | 0 | 0 |
| Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- | 0 | 0 | 0 |
| Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- | 0 | 0 | 0 |
| Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- | 0 | 0 | 0 |
Raw Estimates
This tab shows the raw GST estimates — the density matrices, POVM effects, and process matrices that comprise the estimated gateset. These are explicitly gauge-dependent, and most reports include multiple gauge optimizations
that correspond to slightly different (but physically equivalent and indistinguishable) representations of the operations. Usually, these raw estimates are less useful than the derived properties and decompositions shown elsewhere, but sometimes it's useful to see them. Furthermore, it's possible (at least in some versions of the report) to download the raw gateset in machine-readable form, in order to do calculations and simulations with it.
| Operator | Target Matrix | Estimated Matrix | Target Eigenvals | Estimated Eigenvals |
|---|---|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.95524 \\ 0.02952 \\ 0.014135 \\ 0.001105 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003372 \\ 0.004574 \\ 0.004103 \\ 0.002843 \end{pmatrix} $ | ||
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.981973 \\ 0.075582 \\ 0.034043 \\ 0.011406 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003517 \\ 0.005059 \\ 0.00463 \\ 0.003248 \end{pmatrix} $ | ||
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.948419 \\ 0.075281 \\ 0.007969 \\ 0.009961 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003238 \\ 0.005015 \\ 0.004419 \\ 0.002907 \end{pmatrix} $ | ||
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.893266 \\ 0.036566 \\ 0.007521 \\ 0.004568 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003411 \\ 0.005236 \\ 0.005163 \\ 0.00343 \end{pmatrix} $ | ||
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0.878734 \\ -0.000001 \\ 0.02221 \\ 0.012501 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004112 \\ 0.002991 \\ 0.005177 \\ 0.005088 \end{pmatrix} $ |
| Operator | Target Matrix | Estimated Matrix | Target Eigenvals | Estimated Eigenvals |
|---|---|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.937427 \\ 0.036235 \\ 0.0186 \\ 0.007738 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004092 \\ 0.006181 \\ 0.003262 \\ 0.003685 \end{pmatrix} $ | ||
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.927687 \\ 0.042684 \\ 0.026423 \\ 0.003206 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004141 \\ 0.005683 \\ 0.005483 \\ 0.003348 \end{pmatrix} $ | ||
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.931208 \\ 0.02608 \\ 0.042712 \\ 2\times 10^{-9} \end{pmatrix} $ ± $ \begin{pmatrix} 0.003727 \\ 0.005822 \\ 0.004913 \\ 0.005182 \end{pmatrix} $ | ||
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0.931078 \\ 0.040953 \\ 0.00064 \\ 0.027329 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003293 \\ 0.00658 \\ 0.003252 \\ 0.010916 \end{pmatrix} $ | ||
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0.925533 \\ 0.001502 \\ 0.045588 \\ 0.027377 \end{pmatrix} $ ± $ \begin{pmatrix} 0.006267 \\ 0.005366 \\ 0.007728 \\ 0.007726 \end{pmatrix} $ |
| Operator | Target Matrix | Estimated Matrix | Target Eigenvals | Estimated Eigenvals |
|---|---|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | ||
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | ||
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | ||
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | ||
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ |
targetlogic gates. Each gate is represented as a d^2\times d^2 superoperator that acts by matrix multiplication on vectors in the vector space \mathcal{B}(\mathcal{H}) of operators. Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue), and hovering the pointer over a matrix element will pop up its precise numerical value. Note that it is impossible to discern even order-1%% deviations from the ideal in this view; that's what other analyses (especially the Gate Error Generators tab) are for.
| Gate | Target Superoperator (Tensor-product basis with components pp, pp basis) | Estimated Superoperator (Tensor-product basis with components pp, pp basis) | 95% C.I. half-width |
|---|---|---|---|
| [] | |||
| Gxpi2:1 | |||
| Gxpi2:0 | |||
| Gypi2:1 | |||
| Gypi2:0 | |||
| Gcphase:0:1 |
| Gate | Target Superoperator (Tensor-product basis with components pp, pp basis) | Estimated Superoperator (Tensor-product basis with components pp, pp basis) | 95% C.I. half-width |
|---|---|---|---|
| [] | |||
| Gxpi2:1 | |||
| Gxpi2:0 | |||
| Gypi2:1 | |||
| Gypi2:0 | |||
| Gcphase:0:1 |
| Gate | Target Superoperator (Tensor-product basis with components pp, pp basis) | Estimated Superoperator (Tensor-product basis with components pp, pp basis) |
|---|---|---|
| [] | ||
| Gxpi2:1 | ||
| Gxpi2:0 | ||
| Gypi2:1 | ||
| Gypi2:0 | ||
| Gcphase:0:1 |
Gate Decompositions
This tab presents several decompositions
of the process matrices shown on the Raw Estimates
tab. These are derived properties of the process matrices that aren't directly interpretable as error metrics, but help understand both the overall observed/estimated behavior of the gates and how they differ from the targets. Although the tables on this page do not compare the estimated gates' properties directly to those of the ideal targets, many reports include an analysis of the target gates as well, which can be accessed (and compared directly to the GST estimates) through the Estimates
dropdown menu on the sidebar. Also, since these properties are all at least mildly gauge-dependent, it may be useful to examine different gauge-optimization choices using that dropdown menu on the sidebar.
rotation axisis basically the Hamiltonian that generated the gate. The angles between the various gates' rotation axes are computed from the dot products between them.
| Gate | Ham. Evals. | Rotn. angle | Rotn. axis | Log Error | Axis angle w/[] | Axis angle w/Gxpi2:1 | Axis angle w/Gxpi2:0 | Axis angle w/Gypi2:1 | Axis angle w/Gypi2:0 | Axis angle w/Gcphase:0:1 |
|---|---|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 0.00266 \\ 0.001147 \\ -0.002298 \\ -0.000792 \end{pmatrix} $ π | 0.003781π | 0 | 0.470825π | 0.438107π | 0.607088π | 0.559357π | 0.329304π | ||
| Gxpi2:1 | $ \begin{pmatrix} 0.247197 \\ 0.248756 \\ 0.250812 \\ 0.252435 \end{pmatrix} $ π | 0.499616π | 0 | 0.470825π | 0.501024π | 0.500168π | 0.499391π | 0.501865π | ||
| Gxpi2:0 | $ \begin{pmatrix} 0.253884 \\ 0.248581 \\ -0.253015 \\ -0.249917 \end{pmatrix} $ π | 0.502717π | 0 | 0.438107π | 0.501024π | 0.497802π | 0.497077π | 0.494976π | ||
| Gypi2:1 | $ \begin{pmatrix} 0.252108 \\ 0.247787 \\ -0.251711 \\ -0.248462 \end{pmatrix} $ π | 0.500049π | 0 | 0.607088π | 0.500168π | 0.497802π | 0.496973π | 0.503605π | ||
| Gypi2:0 | $ \begin{pmatrix} -0.248525 \\ -0.252731 \\ 0.252367 \\ 0.250096 \end{pmatrix} $ π | 0.501872π | 0 | 0.559357π | 0.499391π | 0.497077π | 0.496973π | 0.490045π | ||
| Gcphase:0:1 | $ \begin{pmatrix} 0.593593 \\ -0.591931 \\ 0.105673 \\ -0.111969 \end{pmatrix} $ π | 0.852314π | 0 | 0.329304π | 0.501865π | 0.494976π | 0.503605π | 0.490045π |
| Gate | Ham. Evals. | Rotn. angle | Rotn. axis | Log Error | Axis angle w/[] | Axis angle w/Gxpi2:1 | Axis angle w/Gxpi2:0 | Axis angle w/Gypi2:1 | Axis angle w/Gypi2:0 | Axis angle w/Gcphase:0:1 |
|---|---|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 0.003348 \\ -0.003917 \\ 0.000431 \\ -0.001474 \end{pmatrix} $ π | 0.005377π | 0 | 0.549453π | 0.399814π | 0.553346π | 0.495403π | 0.281286π | ||
| Gxpi2:1 | $ \begin{pmatrix} 0.246806 \\ 0.252906 \\ 0.25054 \\ 0.24964 \end{pmatrix} $ π | 0.499965π | 0 | 0.549453π | 0.500788π | 0.500055π | 0.499253π | 0.502075π | ||
| Gxpi2:0 | $ \begin{pmatrix} 0.257141 \\ 0.250655 \\ -0.257142 \\ -0.251529 \end{pmatrix} $ π | 0.50827π | 0 | 0.399814π | 0.500788π | 0.495675π | 0.495578π | 0.49534π | ||
| Gypi2:1 | $ \begin{pmatrix} 0.253608 \\ 0.24795 \\ -0.252596 \\ -0.249065 \end{pmatrix} $ π | 0.501632π | 0 | 0.553346π | 0.500055π | 0.495675π | 0.494774π | 0.503258π | ||
| Gypi2:0 | $ \begin{pmatrix} 0.256245 \\ 0.249399 \\ -0.251106 \\ -0.253576 \end{pmatrix} $ π | 0.50519π | 0 | 0.495403π | 0.499253π | 0.495578π | 0.494774π | 0.4906π | ||
| Gcphase:0:1 | $ \begin{pmatrix} 0.59068 \\ -0.592674 \\ 0.108027 \\ -0.109364 \end{pmatrix} $ π | 0.850762π | 0 | 0.281286π | 0.502075π | 0.49534π | 0.503258π | 0.4906π |
| Gate | Ham. Evals. | Rotn. angle | Rotn. axis | Log Error | Axis angle w/[] | Axis angle w/Gxpi2:1 | Axis angle w/Gxpi2:0 | Axis angle w/Gypi2:1 | Axis angle w/Gypi2:0 | Axis angle w/Gcphase:0:1 |
|---|---|---|---|---|---|---|---|---|---|---|
| [] | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π | 0π | 0 | -- | -- | -- | -- | -- | ||
| Gxpi2:1 | $ \begin{pmatrix} 0.25 \\ 0.25 \\ 0.25 \\ 0.25 \end{pmatrix} $ π | 0.5π | 0 | -- | 0.5π | 0.5π | 0.5π | 0.5π | ||
| Gxpi2:0 | $ \begin{pmatrix} 0.25 \\ 0.25 \\ -0.25 \\ -0.25 \end{pmatrix} $ π | 0.5π | 0 | -- | 0.5π | 0.5π | 0.5π | 0.5π | ||
| Gypi2:1 | $ \begin{pmatrix} -0.25 \\ 0.25 \\ 0.25 \\ -0.25 \end{pmatrix} $ π | 0.5π | 0 | -- | 0.5π | 0.5π | 0.5π | 0.499975π | ||
| Gypi2:0 | $ \begin{pmatrix} -0.25 \\ 0.25 \\ -0.25 \\ 0.25 \end{pmatrix} $ π | 0.5π | 0 | -- | 0.5π | 0.5π | 0.5π | 0.5π | ||
| Gcphase:0:1 | $ \begin{pmatrix} -0.603558 \\ 0.603556 \\ -0.103557 \\ 0.103558 \end{pmatrix} $ π | 0.866031π | 0.005654 | -- | 0.5π | 0.5π | 0.499975π | 0.5π |
| Gate | Choi matrix (Tensor-product basis with components pp, pp basis) | Eigenvalue Magnitudes |
|---|---|---|
| [] | ||
| Gxpi2:1 | ||
| Gxpi2:0 | ||
| Gypi2:1 | ||
| Gypi2:0 | ||
| Gcphase:0:1 |
| Gate | Choi matrix (Tensor-product basis with components pp, pp basis) | Eigenvalue Magnitudes |
|---|---|---|
| [] | ||
| Gxpi2:1 | ||
| Gxpi2:0 | ||
| Gypi2:1 | ||
| Gypi2:0 | ||
| Gcphase:0:1 |
| Gate | Choi matrix (Tensor-product basis with components pp, pp basis) | Eigenvalue Magnitudes |
|---|---|---|
| [] | ||
| Gxpi2:1 | ||
| Gxpi2:0 | ||
| Gypi2:1 | ||
| Gypi2:0 | ||
| Gcphase:0:1 |
Gate Error Generators
This tab presents the error generators for each of the estimated gates. Although these are not especially well-known in the literature, they are (in the pyGSTi authors' opinion) the most useful detailed diagnostic for gate errors. The error generator \mathbb{L} for a noisy gate G with ideal target G_0 is defined by writing G = e^{\mathbb{L}} G_0 . It can be thought of, more or less, as a Lindbladian superoperator that generates the error in the gate — with two caveats. First, it is not necessarily of strict Lindblad form, because the GST-estimated gates may not be CP, and because even if they are, not every CP map is "divisible" (and nondivisible maps are not generated by Lindblad evolution). Second, the generator reported here is a post-gate generator, so it answers the question "If all the noise occurred after the ideal gate, what Lindbladian would generate it?" Finally: the error generators are very definitely gauge-dependent, so caveat emptor (cross-validating any inferences drawn from these generators with some sort of gauge-invariant diagnostic is highly recommended).
error generatorfor each gate. This is (more or less) the Lindbladian \mathbb{L} that describes how the gate is failing to match the target. This error generator is defined by the equation G = e^{\mathbb{L}} G_0 . If it is zero, the estimated gate matches the corresponding ideal target gate. Note that the range of the color scale is dynamically adjusted. Subsequent columns show the result of projecting each generator onto some subspaces of the error generator space. Each corresponds to a different classes of well-known errors: Hamiltonian (coherent) errors, Pauli-stochastic errors, and affine (aka non-unital) errors. The Hamiltonian generators act by commutation with each Pauli basis element B_i, that is \rho \rightarrow -i[B_i, \rho]. Stochastic generators act by conjugation with each basis element, \rho \rightarrow B_i \rho B_i^\dagger. Affine generators act by projecting everything onto a particular basis element, \rho \rightarrow \mathrm{Tr}(\rho) B_i. Roughly speaking, the Hamiltonian projection corresponds precisely to the Hamiltonian that would produce the coherent part of the error, while the Pauli-stochastic generators correspond to the rates of all the Pauli errors (e.g., X errors, Z errors, their 2-qubit counterparts, or whatever is appropriate for the system being analyzed).
| Gate | Error Generator | Hamiltonian Projections | Stochastic Projections | Active\Correlation Projections |
|---|---|---|---|---|
| [] | ||||
| Gxpi2:1 | ||||
| Gxpi2:0 | ||||
| Gypi2:1 | ||||
| Gypi2:0 | ||||
| Gcphase:0:1 |
| Gate | Error Generator | Hamiltonian Projections | Stochastic Projections | Active\Correlation Projections |
|---|---|---|---|---|
| [] | ||||
| Gxpi2:1 | ||||
| Gxpi2:0 | ||||
| Gypi2:1 | ||||
| Gypi2:0 | ||||
| Gcphase:0:1 |
| Gate | Error Generator | Hamiltonian Projections | Stochastic Projections | Active\Correlation Projections |
|---|---|---|---|---|
| [] | ||||
| Gxpi2:1 | ||||
| Gxpi2:0 | ||||
| Gypi2:1 | ||||
| Gypi2:0 | ||||
| Gcphase:0:1 |
Input Summary
This tab presents a grab bag of potentially-useful information about the target gate set and the data set(s).
targetstate preparations (\rho_i) and POVM effects E_i for the device analyzed in this report. SPAM (state preparation and measurement) operations are given as d\times d matrices in the standard (matrix unit) basis of Hilbert space.
| Operator | Matrix | Eigenvals |
|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | |
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | |
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ |
| Operator | Matrix | Eigenvals |
|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | |
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | |
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ |
| Operator | Matrix | Eigenvals |
|---|---|---|
| ρ0 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 00 | $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ | |
| 01 | $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ | |
| 10 | $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ | |
| 11 | $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ |
fiducialcircuits. These circuits precede and follow, respectively, the potentially long germ-to-some-power portion of GST gate sequences, and generate informationally complete input/output ensembles from the native state preparation[s] and measurement.
| Fiducials | ||
|---|---|---|
| # | Prep. | Measure |
| 1 | ||
| 2 | Gxpi2:1 | Gxpi2:1 |
| 3 | Gypi2:1 | Gypi2:1 |
| 4 | Gxpi2:1.Gxpi2:1 | Gxpi2:1.Gxpi2:1 |
| 5 | Gxpi2:0 | Gxpi2:0 |
| 6 | Gxpi2:0.Gxpi2:1 | Gypi2:0 |
| 7 | Gxpi2:0.Gypi2:1 | Gxpi2:0.Gxpi2:0 |
| 8 | Gxpi2:0.Gxpi2:1.Gxpi2:1 | Gxpi2:0.Gxpi2:1 |
| 9 | Gypi2:0 | Gxpi2:0.Gypi2:1 |
| 10 | Gypi2:0.Gxpi2:1 | Gypi2:0.Gxpi2:1 |
| 11 | Gypi2:0.Gypi2:1 | Gypi2:0.Gypi2:1 |
| 12 | Gypi2:0.Gxpi2:1.Gxpi2:1 | |
| 13 | Gxpi2:0.Gxpi2:0 | |
| 14 | Gxpi2:0.Gxpi2:0.Gxpi2:1 | |
| 15 | Gxpi2:0.Gxpi2:0.Gypi2:1 | |
| 16 | Gxpi2:0.Gxpi2:0.Gxpi2:1.Gxpi2:1 | |
germcircuits used in this experiment. Germs are relatively short circuits that get repeated (perhaps many times) in order to amplify various types of qubit errors. The list of germs is often chosen so that all possible types of in-model errors are amplified by at least one germ. Note: it's generally impossible to find a single germ that amplifies all possible errors, except when the gate being studied is the identity operation.
| # | Germ | # | Germ |
|---|---|---|---|
| 1 | [] | 9 | Gxpi2:0.Gxpi2:0.Gypi2:0 |
| 2 | Gxpi2:0 | 10 | Gxpi2:1.Gxpi2:1.Gypi2:1 |
| 3 | Gypi2:0 | 11 | Gxpi2:1.Gypi2:1.Gcphase:0:1 |
| 4 | Gxpi2:1 | 12 | Gcphase:0:1.Gxpi2:1.Gxpi2:0.Gxpi2:0 |
| 5 | Gypi2:1 | 13 | Gxpi2:0.Gxpi2:1.Gypi2:1.Gxpi2:0.Gypi2:1.Gypi2:0 |
| 6 | Gcphase:0:1 | 14 | Gxpi2:0.Gypi2:1.Gxpi2:1.Gypi2:0.Gxpi2:1.Gxpi2:1 |
| 7 | Gxpi2:0.Gypi2:0 | 15 | Gcphase:0:1.Gxpi2:1.Gypi2:0.Gcphase:0:1.Gypi2:1.Gxpi2:0 |
| 8 | Gxpi2:1.Gypi2:1 | 16 | Gypi2:0.Gxpi2:0.Gypi2:1.Gxpi2:0.Gxpi2:1.Gxpi2:0.Gypi2:0.Gypi2:1 |
| Quantity | Value |
|---|---|
| Number of strings | 1702 |
| Gate labels | Gxpi2:1, Gypi2:1, Gxpi2:0, Gypi2:0, Gcphase:0:1 |
| Outcome labels | ('00',), ('01',), ('10',), ('11',) |
| Counts per string | 500 |
| User comment 1 |
target(generally unitary) logic gates. Each has a name starting with
G, and is represented as a d^2\times d^2 superoperator that acts by matrix multiplication on vectors in \mathcal{B}(\mathcal{H}). Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue).
| Gate | Superoperator (Tensor-product basis with components pp, pp basis) |
|---|---|
| [] | |
| Gxpi2:1 | |
| Gxpi2:0 | |
| Gypi2:1 | |
| Gypi2:0 | |
| Gcphase:0:1 |
| Gate | Superoperator (Tensor-product basis with components pp, pp basis) |
|---|---|
| [] | |
| Gxpi2:1 | |
| Gxpi2:0 | |
| Gypi2:1 | |
| Gypi2:0 | |
| Gcphase:0:1 |
| Gate | Superoperator (Tensor-product basis with components pp, pp basis) |
|---|---|
| [] | |
| Gxpi2:1 | |
| Gxpi2:0 | |
| Gypi2:1 | |
| Gypi2:0 | |
| Gcphase:0:1 |
System and pyGSTi parameters
This tab contains a raw dump of system information and various pyGSTi parameters. Its purpose is to stamp this report with parameters that indicate how exactly GST was run to create it, as well as to record the software environment in within which the report creation was run. However, if the core GST computation was done on a different computer, then the software information contained here will be less useful (it describes the environment in which the report was generated, not the one in which the estimate was generated).
| Quantity | Value |
|---|---|
| final_mdc_store | None |
| final_objfn | None |
| final_objfn_builder | |
| final_objfn_cache | None |
| protocol |
| Quantity | Value |
|---|---|
| final_mdc_store | None |
| final_objfn | None |
| final_objfn_builder | |
| final_objfn_cache | None |
| protocol |
| Quantity | Value |
|---|---|
| final_mdc_store | None |
| final_objfn | None |
| final_objfn_builder | |
| final_objfn_cache | None |
| model_test_values | [303924.1791762151, 387138.0523944685, 537975.3913354212, 737897.5922673217] |
| protocol | None |
| raw_objective_values | [151962.08958810754, 193569.02619723426, 268987.6956677106, 368948.7961336608] |
| Label | Time (sec) |
|---|
| Label | Time (sec) |
|---|
| Label | Time (sec) |
|---|
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- Iterative GST: [##################################################] 100.0% 1702 circuits
- Iterative GST Total Time: 815.2s
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
- Iterative GST: [##################################################] 100.0% 1702 circuits
- Iterative GST Total Time: 219.6s
- No standard output recorded
| Quantity | Value |
|---|---|
| pyGSTi version | 0.9.11.1.post2 |
| numpy | 1.25.0 |
| scipy | 1.11.4 |
| matplotlib | 3.6.3 |
| ply | 3.11 |
| cvxopt | 1.3.2 |
| cvxpy | 1.4.1 |
| nose | missing |
| PIL | 10.0.0 |
| psutil | 5.9.5 |
| Python version | 3.10.12 |
| Python type | CPython |
| Python compiler | GCC 12.3.0 |
| Python build | ('main', 'Jun 23 2023 22:40:32') |
| Python branch | |
| Python revision | |
| Platform summary | Linux-5.4.0-155-generic-x86_64-with-glibc2.31 |
| System | Linux |
| Sys Release | 5.4.0-155-generic |
| Sys Version | #172-Ubuntu SMP Fri Jul 7 16:10:02 UTC 2023 |
| Machine | x86_64 |
| Processor | x86_64 |
How to use this report
Welcome to a pyGSTi report! This HTML document provides an interactive view onto a lot of information about one or more gateset tomography (GST) experiments that were analyzed using the pyGSTi software. This Help
tab should help you use this report's interactive features, figure out where to find things, and access the context-sensitive help features embedded throughout the report.
Background
PyGSTi's primary purpose is to ingest GST datasets and find a good estimate of the gateset that generated that data. But pyGSTi can also produce a lot of detailed analyses and visualizations of the estimates that it generates. That's what you'll find in this report. You can inspect the raw estimated gateset too, but if you want to do your own calculations with it — e.g., to simulate experiments or calculate interesting quantities that the pyGSTi authors haven't thought of — then the best way to do that is by using pyGSTi itself in a Jupyter or iPython notebook.
This report's structure
PyGSTi uses HTML for reporting because it's pretty portable and supports interactivity. Interactivity makes it possible to embed a lot of different perspectives and analyses, without overwhelming you with too much information at once or requiring you to scroll through long static (e.g. PDF) documents. In this report, actual content is displayed in the main panel, while navigation tools that let you decide what content to examine are collected in a sidebar on the left. The tables and figures in the main panel are also somewhat interactive (see “Interacting with content” below). Most of them dynamically change what they show depending on the positions of one or more switches - dropdown-menus, button-sets, or sliders. Most switches are located on the sidebar, but some appear in the main panel beneath the figure or table that they control. Note that some content is generated on the fly, so there may be a lag the very first time you view a given tab, while your browser makes plots or renders math formulas.
Choosing what to see via the sidebar
The sidebar provides two distinct ways to control what you see. First, the data analysis is broken up into different tabs that are listed on the sidebar. Use the sidebar to hop between them. Each tab collects a particular category of analysis, presented as tables and figures. Second, if the report contains multiple analyses, the sidebar displays switches that allow you to pick which analysis to display in the main panel. A report can contain: (1) multiple distinct datasets; (2) the results of different estimators (each associated with a given dataset); and (3) multiple distinct but equivalent representations (gauges) for each estimate. You can choose between these options using the drop down menus labeled Dataset
and Estimate
, and the Gauge-Opt.
button group at the bottom of the sidebar. If a switch is missing, the report doesn't contain multiple options of that type. You can hide the sidebar (or make is sticky) by clicking the ⊛ symbol in its upper right corner.
Due to the large amount of data a report can contain, there are options that allow one to omit some of the (usually larger or more data-dense) figures from the report at its creation time. This will result in the report having fewer tabs in the sidebar and/or the word OMITTED being displayed instead of a figure. To see missing tabs or omitted figures, you should ask whoever generated this report to re-generate it with a lower brevity
setting.
Interacting with content
Each tab presents a (hopefully manageable) amount of content arranged into objects — figures and tables — that have some interactive properties. Here are some general tips and rules.
- Resizing: Each object can be resized by dragging its lower right corner.
- Zooming: You can zoom in on plots' axes by clicking and dragging within the figure. Double-clicking, or tapping the house icon that pops up in the upper right when the pointer is over a figure, will reset the axes.
- Exporting: Plots can be saved in PNG format by tapping the camera icon, which only appears when the pointer is over a plot). (User beware: this is a builtin feature of the Plotly library, and we find that sometimes the saved PNG does not look like the original plot, especially in aspect ratio.) Depending on what options were selected when the report was constructed, there may also be links to download plots and tables as PDF, Python
pickle
files, and/or LaTeX (tables only). Plots will have additional download icons next to the camera icon, and tables will have PDF, PKL, and/or TEX links beneath them. PKL files downloaded from plots contain a pickled dictionary of the plotted data, while those downloaded from tables contain a pickled Pandas DataFrame object. - Full descriptive captions for figures and tables can be revealed by clicking on the object's Figure XX or Table XX title.
- Hovering over a colored bar or box will often reveal a tool tip showing the exact number that bar or box represents. Hovering over table headings will bring up descriptive text. In the plots that show per-sequence model violation, hovering over any data point will bring up fairly extensive details about the datum that generated it.
- Clickable pigs: If you see the pyGSTi logo, it's a placeholder for a plot that wasn't automatically generated (usually because this might take a little while); click on the logo to generate the plot.
| Hover over me... | And me! | Click the pig |
|---|---|---|
| Pi | 3.141593 |
Quick guide to Datasets, Estimates, and Gauge Optimizations
The single biggest change from the old PDF report format is the ability to report simultaneously on — and compare — multiple gateset estimates. This report may contain an unlimited number of distinct gatesets. Although they're often all derived from the same dataset, they may not be. For example, a single report could contain:
- datasets from separate GST experiments on each qubit on a chip;
- datasets from two identical GST experiments done at different times;
- datasets from GST experiments on the same system, but with gate implementations;
- a 2-qubit GST dataset together with 1-qubit GST datasets extracted from it;
- many other possibilities.
The sidebar's Dataset
dropdown menu (if present) lets you select a dataset. Then, the Estimate
dropdown (if present) will list all the different estimates that are available for any of the datasets in the report. If you choose an estimate that was not generated for the current dataset (but is listed because it was generated for another dataset), unavailable plots and figures will turn into big "N/A" labels. Different estimates are usually generated by different statistical estimators. PyGSTi usually provides maximum likelihood estimates (although others are certainly possible!), but it can do MLE with no constraints at all (Full
), or constrained to trace-preserving maps (TP
), or constrained to completely positive maps (CPTP
). Some reports include separate *.robust
variations of those estimators in which poorly-fit data were deprecated, and some reports include the target gates themselves (Target
) as an option.
Finally, in order to analyze each estimated gateset, pyGSTi has to choose a representation — a gauge — for it. Since pyGSTi does this gauge-fixing internally by defining an objective function and then finding the gauge that optimizes it, the choice-of-representation is referred to as Gauge Optimization
. A description of the objective function used to generate this gateset appears at the bottom of the sidebar. If the report contains multiple gauge optimizations, you can choose between them by pushing the appropriate button. Choosing a good gauge is hard, and neither pyGSTi nor its users always get it right. If something reported in the Summary
or Gauge-dependent error metrics
tabs looks startling or implausible, it might be due to a poorly chosen gauge. Try a different gauge-optimization choice, or cross-validate whatever you see against things from the Gauge-invariant error metrics
tabs.
What to look at first (and second)
If you're new to pyGSTi reports, this is probably all a bit overwhelming. Don't panic! There's a lot of context-sensitive help, and the pyGSTi authors are always happy to answer questions like What does this mean?
, or Why would I care about this?
But since these reports do contain a lot of stuff, here's a get-started-quickly guide.
Start with the Summary
tab. It will tell you two critical things. First, in Table 3: how close do the gates seem to be to the ideal targets that were specified? Are you doing pretty well, or all messed up for some reason? If whoever did the analysis chose to produce error bars (this can take a lot of computation), they'll appear in this table. Second, the model violation
plots will tell you whether the system seems to be stable and Markovian, or not (in which case, take the metrics in Table 3 with a grain of salt). Don't forget to flip through the available datasets, estimates, and gauge-optimization choices — or at least the ones you care about — while looking at this tab.
Next, you probably want to know one of two things. Either the GST model was NOT badly violated, in which case you want to know more about the errors in the gates.. or it WAS badly violated, in which case you want to know more about what's going wrong.
If you want to know more about the errors, start with Gauge Dependent Error Metrics: Overview
, then take a quick look at Raw Estimates
to confirm that the process matrices look about right, and then spend some quality time with Gate Decompositions
and Gate Error Generators
if you want to really understand what GST thinks that each individual gate is doing. If at any point you see something weird that might be due to a bad choice of gauge (examples include wildly nonpositive SPAM operations, implausibly high diamond norm errors in gates that you strongly believe to be better than that, and significantly negative elements in the Pauli stochastic part of the error generators), try a different gauge optimization. Or, go to the Gauge-invariant error metrics
tabs and try to figure out whether there's something here that confirms or denies whatever effect is bugging you (e.g., if an estimated gate has an eigenvalue bigger than 1, that will produce crazy negative probabilities, and it's not a gauge problem).
On the other hand, if there's a lot of model violation, then you probably want to understand why. The information on the error metrics tabs may or may not be useful — you should be much more cautious about drawing conclusions from them if there's a lot of model violation. To dig into model violation (aka “non-Markovianity”), start with the Model Violation: Overview
tab, which will give you the numbers behind the bar chart from the Summary tab, and also show you whether longer circuits violate the GST model more. (If they do, it's probably non-Markovianity in the gates. If they don't, it's probably something nastier like bistability, slow drift in SPAM operations, or corrupted data). Next, take a deep breath and dig into the “Per-sequence detail” tab, which will show you the (quantitative) inconsistency of every individual circuit with this estimate. Interpreting these charts is a bit of an art, but clusters of red boxes usually indicate that something related to the location of the cluster was suffering drift and/or non-Markovianity.